Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 6-2 MyStatLab: Module Six Problem Set 1. Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. Do the two variables have a linear relationship? A. The data points do not have a linear relationship because they lie mainly in a straight line. C. The data points have a linear relationship because they lie mainly in a straight line. Response Student: allan cranford Date: 9/26/16 400 300 200 100 0 0 2 4 6 8 Explanatory B. The data points have a linear relationship because they do not lie mainly in a straight line. D. The data points do not have a linear relationship because they do not lie mainly in a straight line. If the relationship is linear do the variables have a positive or negative association? A. The variables have a positive association. B. The variables have a negative association. 2. Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. Do the two variables have a linear relationship? A. The data points have a linear relationship because they do not lie mainly in a straight line. C. The data points have a linear relationship because they lie mainly in a straight line. B. The two variables have a positive association. C. None of the above 30 20 10 0 0 20 Explanatory B. The data points do not have a linear relationship because they lie mainly in a straight line. D. The data points do not have a linear relationship because they do not lie mainly in a straight line. Do the two variables have a positive or a negative association? A. The two variables have a negative association. Response C. The relationship is not linear. 40 10 3. For the accompanying data set, (a) draw a scatter diagram of the data, (b) compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y. 1 Click the icon to view the data set. 2 Click the icon to view the critical values table. (a) Draw a scatter diagram of the data. Choose the correct graph below. A. y 10 0 B. 0 y 10 x 10 0 C. y 10 x 0 0 10 D. y 10 x 0 0 10 x 0 10 (b) Compute the correlation coefficient. The correlation coefficient is r = . (Round to three decimal places as needed.) (c) Determine whether there is a linear relation between x and y. Because the correlation coefficient is (1) and the absolute value of the correlation coefficient, , is (2) than the critical value for this data set, relation exists between x and y. (Round to three decimal places as needed.) 1: Data set x y 7 8 2: critical values for the correlation coefficient 6 2 1 6 7 9 9 5 Critical Values for Correlation Coefficient , (3) linear n 3 0.997 5 0.878 4 6 7 8 9 0.950 0.811 0.754 0.707 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 (1) positive negative (2) greater not greater (3) no a negative a positive 4. A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children, measures their height and head circumference, and obtains the data shown in the table. Head Height (inches)Circumference (inches) 27.25 17.5 25 17 26 17.2 25.5 17 27.5 17.4 26.25 17.4 25.75 17.1 27 17.4 Click here to see the Table of Critical Values for Correlation Coefficient. 3 (a) If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is the response variable. The explanatory variable is head circumference and the response variable is height. The explanatory variable is height and the response variable is head circumference. B. 16.9 25 28 Circ. (in.) C. 17.6 Circ. (in.) 17.6 Circ. (in.) Height (in.) A. 16.9 25 28 Height (in.) 28 25 16.9 17.6 Height (in.) D. Height (in.) (b) Draw a scatter diagram. Which of the following represents the data? 28 25 16.9 17.6 Circ. (in.) (c) Compute the linear correlation coefficient between the height and head circumference of a child. r= (Round to three decimal places as needed.) (d) Does a linear relation exist between height and head circumference? A. Yes, there appears to be a positive linear association because r is positive and is greater than the critical value. B. Yes, there appears to be a positive linear association because r is positive and is less than the critial value. C. Yes, there appears to be a negative linear association because r is negative and is less than the negative of the critical value. D. No, there is no linear association since r is positive and is less than the critical value. 3: Data Table Critical Values for Correlation Coefficient n 3 0.997 5 0.878 4 6 7 8 9 0.950 0.811 0.754 0.707 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 5. Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of 3 females and 3 males and measured their MRI counts and IQ scores. The data is reported on the right. Females MRI IQ 866,664 132 790,620 135 856,473 141 Males MRI 965,355 949,395 1,038,438 Treat the MRI count as the explanatory variable. Compute the linear correlation coefficient between MRI count and IQ for both the males and the females. Do you believe that MRI count and IQ are linearly related? The linear correlation coefficient for females is . IQ 132 141 138 The linear correlation coefficient for males is . (Round to three decimal places as needed.) Are MRI count and IQ linearly related? The linear correlation coefficient for females is close to (1) so (2) linear relation exists between MRI count and IQ for females. The linear correlation coefficient for males is close to (3) so (4) linear relation exists between MRI count and IQ for males. (1) (2) 0, 1, 1, a negative no (3) a positive (4) 1, 1, 0, a negative a positive no 6. For the data set below, (a) Determine the least-squares regression line. (b) Graph the least-squares regression line on the scatter diagram. x y 4 7 5 8 6 9 7 14 9 16 (a) Determine the least-squares regression line. y= x+( ) (Round to four decimal places as needed.) (b) Choose the correct graph below. A. y 10 0 B. 0 y 10 x 18 0 C. 0 y 17 x 17 0 D. 0 y 18 x 10 0 0 x 10 7. For the data set below, (a) Determine the least-squares regression line. (b) Compute the sum of the squared residuals for the least-squares regression line. x y 10 95 20 91 30 91 40 69 50 58 (a) Determine the least-squares regression line. y= x+ (Round to four decimal places as needed.) (b) The sum of the squared residuals is (Round to two decimal places as needed.) . 8. A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and grade-point average, y. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is y = 0.0549x + 2.9177. (a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is (Round to the nearest hundredth as needed.) . (b) Interpret the slope. For each additional hour that a student spends playing video games in a week, the grade-point average will (1) by points, on average. (c) If appropriate, interpret the y-intercept. A. The average number of video games played in a week by students is 2.9177. B. The grade-point average of a student who does not play video games is 2.9177. C. It cannot be interpreted without more information. (d) A student who plays video games 7 hours per week has a grade-point average of 2.62. Is the student's grade-point average above or below average among all students who play video games 7 hours per week? The student's grade-point average is (2) (1) increase decrease (2) above below average for those who play video games 7 hours per week. 9. An author of a book discusses how statistics can be used to judge both a baseball player's potential and a team's ability to win games. One aspect of this analysis is that a team's on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For a certain baseball season, winning percentage, y, and on-base percentage, x, are linearly related by the least-squares regression equation y = 2.94x 0.4877. Complete parts (a) through (d). (a) Interpret the slope. Choose the correct answer below. A. For each percentage point increase in winning percentage, the on-base percentage will increase by 2.94 percentage points, on average. B. For each percentage point increase in on-base percentage, the winning percentage will increase by 2.94 percentage points, on average. C. For each percentage point increase in winning percentage, the on-base percentage will decrease by 2.94 percentage points, on average. D. For each percentage point increase in on-base percentage, the winning percentage will decrease by 2.94 percentage points, on average. (b) For this baseball season, the lowest on-base percentage was 0.318 and the highest on-base percentage was 0.362. Does it make sense to interpret the y-intercept? Yes No (c) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.240? No, it would be a bad idea. Yes, it would be a good idea. (d) A certain team had an on-base percentage of 0.326 and a winning percentage of 0.546. What is the residual for that team? How would you interpret this residual? The residual for the team is . (Round to four decimal places as needed.) How would you interpret this residual? A. This residual indicates that the winning percentage of the team is above average for teams with a winning percentage of 0.546. B. This residual indicates that the winning percentage of the team is below average for teams with an on-base percentage of 0.326. C. This residual indicates that the winning percentage of the team and the on-base percentage of other teams do not vary. D. This residual indicates that the winning percentage of the team is above average for teams with an on-base percentage of 0.326. 10. Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researchers wanted to know whether consumption of cola is associated with lower bone mineral density in women. The data shown in the accompanying table represent the typical number of cans of soda consumed in a week and the bone mineral density of the femoral neck for a sample of 15 women. The data were collected through a prospective cohort study. Complete parts (a) through (f). 4 Click the icon to view the data table. 5 Click the icon to view a table of critical values for the correlation coefficient. (a) Find the least-squares regression line treating cola consumption per week as the explanatory variable. Choose the correct answer below. A. The least-squares regression line is y = 0.8869x + 0.0031. B. The least-squares regression line is y = 0.0031x + 0.8869. C. The least-squares regression line is y = 0.8869x 0.0031. D. The least-squares regression line is y = 0.0031x 0.8869. (b) Interpret the slope. For each additional cola consumed per week, bone mineral density will (1) g / cm2 , on average. (2) by (c) Interpret the intercept. Choose the correct answer below. A. For each additional cola consumed per week, bone mineral density will decrease by 0.0031 g/cm2 , on average. B. For a woman who does not drink cola, bone mineral density will be 0.0031 g/cm2 . C. It is not appropriate to interpret the y-intercept. It is outside the scope of the model. D. For a woman who does not drink cola, bone mineral density will be 0.8869 g/cm2 . (d) Predict the bone mineral density of the femoral neck of a woman who consumes four colas per week. The predicted value of the bone mineral density of the femoral neck of this woman is four decimal places as needed.) 2 g / cm . (Round to 2 (e) The researchers found a woman who consumed four colas per week to have a bone mineral density of 0.873 g/cm . Is this woman's bone mineral density above or below average among all women who consume four colas per week? Above average Below average (f) Would you recommend using the model found in part (a) to predict the bone mineral density of a woman who consumes two cans of cola per day? Yes No 4: Data Table Number of Colas per Week 0 0 1 1 2 2 3 3 Bone Mineral Density (g/cm ) Number of Colas per Week Density (g/cm2 ) 0.884 5 0.875 2 0.897 0.891 0.879 0.888 0.871 0.868 0.876 5: Critical Values for Correlation Coefficient 4 5 6 7 7 8 Bone Mineral 0.873 0.871 0.867 0.862 0.872 0.865 Full data set (1) increase decrease (2) 0.0031 1.0054 0.5423 0.8869 11. The given data represent the total compensation for 10 randomly selected CEOs and their company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r = 0.2365. What would be the predicted stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million? 6 Click the icon to view the compensation and stock performance data. 7 Click the icon to view a table of critical values for the correlation coefficient. What would be the predicted stock return for a company whose CEO made $15 million? % (Type an integer or decimal rounded to one decimal place as needed.) What would be the predicted stock return for a company whose CEO made $25 million? % (Type an integer or decimal rounded to one decimal place as needed.) 6: CEO Compensation and Stock Performance Compensation (millions of dollars) 26.42 5.85 12.08 30.87 13.19 79.88 19.06 31.34 12.44 8.39 25.88 4.46 12.03 3.04 14.48 10.92 14.67 11.45 17.93 7: Critical Values for Correlation Coefficient Stock Return (%) 3.84 12. Analyze the residual plot below and identify which, if any, of the conditions for an adequate linear model is not met. Residuals 20 0 -20 5 15 Explanatory 25 Which of the conditions below might indicate that a linear model would not be appropriate? Patterned residuals None Constant error variance Outlier 13. The following data represent the time between eruptions and the length of eruption for 8 randomly selected geyser eruptions. Complete parts (a) and (b) below. Click here to view a scatter plot of the data.8 Click here to view a residual plot of the data.9 Time, x 12.18 11.78 11.99 12.19 Length, y 1.89 1.80 1.87 1.82 Time, x 11.46 11.62 12.06 11.35 Length, y 1.67 1.72 1.86 1.66 (a) Does the residual plot confirm that the relation between time between eruptions and length of eruption is linear? A. Yes. The plot of the residuals shows a discernible pattern, implying that the explanatory and response variables are linearly related. B. Yes. The plot of the residuals shows no discernible pattern, so a linear model is appropriate. C. No. The plot of the residuals shows no discernible pattern, implying that the explanatory and response variables are not linearly related. D. No. The plot of the residuals shows that the spread of the residuals is increasing or decreasing, violating the requirements of a linear model. (b) The coefficient of determination is found to be 88.1%. Choose the best interpretation below. A. The least-squares regression equation does not explain 88.1% of the variation in time between eruptions. B. The least-squares regression equation explains 88.1% of the variation in time between eruptions. C. The least-squares regression equation does not explain 88.1% of the variation in length of eruption. D. The least-squares regression equation explains 88.1% of the variation in length of eruption. 8: Scatter plot of eruption data. 2 y 1.9 1.8 1.7 1.6 1.5 11 9: Residual plot of eruption data. 11.4 11.8 12.2 x 12.6 0.2 y 0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2 11 11.4 11.8 12.2 x 12.6 14. The time it takes for a planet to complete its orbit around a particular star is called the planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts (a) through (e). 10 Click the icon to view the data table. (a) Draw a scatter diagram of the data treating distance from the star as the explanatory variable. Choose the correct graph below. A. B. Sidereal Year 250 0 Sidereal Year 250 125 C. 125 0 2000 4000 0 Distance (millions of miles) Distance (millions of miles) 4000 2000 0 2000 0 4000 0 Distance (millions of miles) 125 Sidereal Year 250 (b) Determine the correlation between distance and sidereal year. The correlation between distance and sidereal year is (Round to three decimal places as needed.) . Does this imply a linear relation between distance and sidereal year? No Yes (c) Compute the least-squares regression line. Choose the correct answer below. y = 0.0656x + 12.661 y = 0.0656x + 12.661 y = 0.0656x + 132.621 y = 0.0656x 12.661 (d) Plot the residuals against the distance from the star. Choose the correct graph below. A. 20 B. Residual 20 0 -20 C. Residual 500 0 0 2000 4000 Distance (millions of miles) -20 250 0 2000 4000 Distance (millions of miles) (e) Do you think the least-squares regression line is a good model? Yes No Residual 0 0 2000 4000 Distance (millions of miles) 10: Data Table Planet Planet 1 Planet 2 Planet 3 Distance from the Star, x (millions of miles) Sidereal Year, y 67 0.62 36 0.22 93 1.00 Planet 4 142 Planet 6 887 Planet 5 483 Planet 7 1,785 Planet 9 3,675 Planet 8 2,797 1.88 11.8 29.3 82.0 165.0 248.0 Student: allan cranford Date: 9/26/16 Instructor: Basu Dipanker Course: MAT-240-Q6622-16EW6 Assignment: 7-2 MyStatLab: Module Seven Problem Set 1. Suppose a least-squares regression line is given by y = 4.302x 3.293. What is the mean value of the response variable if x = 20? y 20 = (Round to one decimal place as needed.) 2. In the least-squares regression model, yi = 1 xi + 0 + i , i is a random error term with mean ____ and standard deviation = ____. i In the least-squares regression model, yi = 1 xi + 0 + i , i is a random error term with mean (1) standard deviation = (2) i (1) 0 1 (2) . 0. 1. . and 3. For the data set shown below, complete parts (a) through (d) below. x 3 y 5 4 5 7 7 8 13 8 14 (a) Find the estimates of 0 and 1 . 0 b0 = 1 b1 = (Round to three decimal places as needed.) (Round to three decimal places as needed.) (b) Compute the standard error, the point estimate for . se = (Round to four decimal places as needed.) (c) Assuming the residuals are normally distributed, determine sb . 1 sb = 1 (Round to three decimal places as needed.) (d) Assuming the residuals are normally distributed, test H0 : 1 = 0 versus H1 : 1 0 at the = 0.05 level of significance. Use the P-value approach. The P-value for this test is . (Round to three decimal places as needed.) Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below. A. Reject H0 . There is sufficient evidence at the = 0.05 level of significance to conclude that a linear relation exists between x and y. B. Do not reject H0 . There is not sufficient evidence at the = 0.05 level of significance to conclude that a linear relation exists between x and y. C. Do not reject H0 . There is sufficient evidence at the = 0.05 level of significance to conclude that a linear relation exists between x and y. D. Reject H0 . There is not sufficient evidence at the = 0.05 level of significance to conclude that a linear relation exists between x and y. 4. For the data set shown below, complete parts (a) through (d) below. x y 20 30 40 98 97 93 50 60 83 70 (a) Use technology to find the estimates of 0 and 1 . 0 b0 = 1 b1 = (Round to two decimal places as needed.) (Round to two decimal places as needed.) (b) Use technology to compute the standard error, the point estimate for . se = (Round to four decimal places as needed.) (c) Assuming the residuals are normally distributed, use technology to determine sb . 1 sb = 1 (Round to four decimal places as needed.) (d) Assuming the residuals are normally distributed, test H0 : 1 = 0 versus H1 : 1 0 at the = 0.05 level of significance. Use the P-value approach. Determine the P-value for this hypothesis test. P-value = (Round to three decimal places as needed.) Which of the following conclusions is correct? A. Do not reject H0 and conclude that a linear relation exists between x and y. B. Do not reject H0 and conclude that a linear relation does not exist between x and y. C. Reject H0 and conclude that a linear relation does not exist between x and y. D. Reject H0 and conclude that a linear relation exists between x and y. 5. The data in the accompanying table represent the rate of return of a certain company stock for 11 months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts (a) through (d) below. 1 Click the icon to view the data table. (a) Treating the rate of return of the index as the explanatory variable, x, use technology to determine the estimates of 0 and 1 . The estimate of 0 is . The estimate of 1 is . (Round to four decimal places as needed.) (Round to four decimal places as needed.) (b) Assuming the residuals are normally distributed, test whether a linear relation exists between the rate of return of the index, x, and the rate of return for the company stock, y, at the = 0.10 level of significance. Choose the correct answer below. State the null and alternative hypotheses. A. H0 : 1 = 0 H1 : 1 > 0 B. H0 : 1 = 0 H1 : 1 0 C. H0 : 0 = 0 H1 : 0 0 D. H0 : 0 = 0 H1 : 0 > 0 Determine the P-value for this hypothesis test. P-value = (Round to three decimal places as needed.) State the appropriate conclusion at the = 0.10 level of significance. Choose the correct answer below. A. Reject H0 . There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. B. Do not reject H0 . There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. C. Reject H0 . There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. D. Do not reject H0 . There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. (c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: Upper bound: (Round to four decimal places as needed.) (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.15%? The mean rate of return for the company stock if the rate of return of the index is 3.15% is (Round to three decimal places as needed.) %. 1: Rate of Return Month Apr-07 May-07 Rates of return of the index, x 4.33 3.35 Jun-07 1.78 Aug-07 1.29 Jul-07 Sept-07 Oct-07 3.20 3.58 5.09 0.54 2.88 2.69 7.41 4.83 0.86 2.37 4.40 Jan-08 6.12 Feb-08 3.38 1.48 Nov-07 Dec-07 Rates of return of the company stock, y 3.48 2.38 4.27 3.77 6. A doctor wanted to determine whether there is a relation between a male's age and his HDL (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor is the in the data table below. Complete parts (a) through (f) below. 2 Click the icon to view the data obtained by the doctor. (a) Draw a scatter diagram of the data, treating age as the explanatory variable. What type of relation, if any, appears to exist between age and HDL cholesterol? A. There does not appear to be a relation. B. The relation appears to be nonlinear. C. The relation appears to be linear. (b) Determine the least-squares regression equation from the sample data. y= x+ (Round to three decimal places as needed.) (c) Are there any outliers or influential observations? Yes No (d) Assuming the residuals are normally distributed, test whether a linear relation exists between age and HDL cholesterol levels at the = 0.01 level of significance. What are the null and alternative hypotheses? A. H0 : 1 = 0; H1 : 1 > 0 B. H0 : 1 = 0; H1 : 1 0 C. H0 : 1 = 0; H1 : 1 < 0 Use technology to compute the P-value. Use the Tech Help button for further assistance. The P-value is . (Round to three decimal places as needed.) What conclusion can be drawn at = 0.01 level of significance? A. Reject the null hypothesis because the P-value is less than = 0.01. B. Do not reject the null hypothesis because the P-value is less than = 0.01. C. Do not reject the null hypothesis because the P-value is greater than = 0.01. D. Reject the null hypothesis because the P-value is greater than = 0.01. (e) Assuming the residuals are normally distributed, construct a 95% confidence interval about the slope of the true least-squares regression line. Lower Bound = Upper Bound = (Round to three decimal places as needed.) (f) For a 42-year-old male patient who visits the doctor's office, would using the least-squares regression line obtained in part (b) to predict the HDL cholesterol of this patient be recommended? If the null hypothesis was rejected, that means that this least-squares regression line can accurately predict the HDL cholesterol of a patient. If the null hypothesis was not rejected, that means the least-squares regression line cannot accurately predict the HDL cholesterol of a patient. Should this least-squares regression line be used to predict the patient's HDL cholesterol? Choose the correct answer below. A. No, because the null hypothesis was rejected. B. Yes, because the null hypothesis was not rejected. C. No, because the null hypothesis was not rejected. D. Yes, because the null hypothesis was rejected. A good estimate for the HDL cholesterol of this patient is (Round to two decimal places as needed.) 2: Age vs. HDL Cholesterol data Age, x 40 44 46 34 55 50 59 60 27 HDL Cholesterol, y 55 55 35 55 34 41 44 38 45 Age, x 37 64 28 53 28 53 47 39 . HDL Cholesterol, y 44 63 51 36 47 39 53 28 7. What do the y-coordinates on the least-squares regression line represent? Choose the correct answer below. A. The y-coordinates represent the maximum expected value of the response variable for any given value of the explanatory variable. B. The y-coordinates represent the minimum expected value of the response variable for any given value of the explanatory variable. C. The y-coordinates represent the mean value of the response variable for any given value of the explanatory variable. D. The y-coordinates represent the values of the explanatory variable. 8. Suppose a multiple regression model is given by y = 4.64x + 8.32x + 30.81. What would an interpretation of the 1 2 coefficient of x1 be? Fill in the blank below. An interpretation of the coefficient of x1 would be, "if x1 increases by 1 unit, then the response variable will decrease by units, on average, while holding x2 constant." 9. The multiple regression equation y = 5 x + 8x is obtained from a set of sample data. Complete parts (a) through (e). 1 2 (a) Interpret the slope coefficient for x1 . Choose the correct answer below. A. The slope coefficient of x is 1. This indicates that y will decrease 1 unit, for every one unit increase 1 in x1 , x2 remains constant. B. The slope coefficient of x is 5. This indicates that y will increase 5 units, for every one unit increase in 1 x1 , x2 remains constant. C. The slope coefficient of x is 1. This indicates that y will increase 1 unit, for every one unit increase 1 in x1 , x2 remains constant. Interpret the slope coefficient for x2 . Choose the correct answer below. A. The slope coefficient of x is 8. This indicates that y will increase 8 units, for every one unit increase in 2 x2 , x1 remains constant. B. The slope coefficient of x is 5. This indicates that y will increase 5 units, for every one unit increase in 1 x1 , x2 remains constant. C. The slope coefficient of x is 8. This indicates that y will increase 1 / 8 units, for every one unit increase 2 in x2 , x1 remains constant. (b) Determine the regression equation with x1 = 10. Choose the correct answer below. y = 30 + 8x2 y = 5 + 8x2 y = 5 + 8x2 y = 5 + 8x1 Graph the regression equation with x1 = 10. Choose the correct graph below. A. 80 B. y 80 x -80 80 -80 C. y 80 x -80 80 (c) Determine the regression equation with x1 = 15. Choose the correct answer below. y = 32 + 8x2 y = 10 + 8x2 x -80 -80 y 80 -80 y = 5 + 8x2 y = 5 + 8x1 Graph the regression equation with x1 = 15. Choose the correct graph below. A. 80 B. y 80 x -80 80 y 80 x -80 -80 C. 80 y x -80 -80 80 -80 (d) Determine the regression equation with x1 = 20. Choose the correct answer below. y = 45 + 8x2 y = 5 + 8x2 y = 15 + 8x2 y = 5 + 8x1 Graph the regression equation with x1 = 20. Choose the correct graph below. A. 80 B. y 80 x -80 80 -80 C. y 80 x -80 80 -80 x -80 80 -80 (e) What is the effect of changing the value x1 on the graph of the regression equation? No changes Changes in the y-intercept Changes in the slope y 10. Determine if there is a linear relation among air temperature x1 , wind speed x2 , and wind chill y. The following data show the measured values for various days. x1 10 30 30 0 0 20 x2 50 y 50 62 8 30 30 10 30 30 30 20 44 22 70 44 88 44 6 96 104 64 32 40 0 10 10 40 80 50 20 20 70 100 30 20 90 (a) Find the least-squares regression equation y = b0 + b1 x1 + b2 x2 , where x1 is air temperature and x2 is wind speed, and y is the response variable, wind chill. y= + x1 + x2 (Round to three decimal places as needed.) (b) Draw residual plots to assess the adequacy of the model. Create the residual plot for air temperature. Choose the correct graph below. A. 10 -40 B. y 10 x -10 40 -40 C. y 10 x -10 40 -40 y 10 x -10 D. 40 -40 y x -10 40 Create the residual plot for wind speed. Choose the correct graph below. A. 10 -10 0 B. y 10 x 120 -10 0 C. y 10 x 120 -10 0 D. y 10 x 120 -10 0 y x 120 What might you conclude based on the plot of residuals against wind speed? Choose the correct answer below. A. The plot shows no discernable pattern, so the linear model is inappropriate. B. The plot shows a discernable pattern, so the linear model is inappropriate. C. The plot shows a discernable pattern, so the linear model is appropriate. D. The plot shows no discernable pattern, so the linear model is appropriate