The average daily temperature (in degress Farenheit) and the number of visitors to a local beach during each week of the season are measured by a researcher. The goal is to determine if number of weekly visitors can be predicated based on the average daily temperature ofgiven week. Beach Visitors 600 525 450 375 300 225 150 75 Visitors 80 84 88 92 96 Average Daily Temperature ('F} In this study, the response variable is O a number of visitors. 0 b ave rage daily temperature. 0 c not applicable because it is not being studied as a cause and effect relationship. 0 d the measuring instrument used to measure temperature. Suppose we fit the least-squares regression line to a set of data and calcuate the residuals. Ifa plot of the residuals shows a pattern, 0 a a non~linear regression model would be a better fit for the data. 0 b a straight line is a good summary for the data. 0 c the correlation must be zero. 0 d there is a definite cause and effect relationship. The following scatter plot presents data on an individual's Body Mass Index and their percent of body fat. Scatterplot of %Fat vs BM] 15 Ill 15 3a 35 BM From the scatterplot, what must the correlation coefficient be? 0 a r=0.'|9 O b r=0.74 O c =o.19 0 d r=-0.74 A study gathers data on the brain function of teenagers and routine exercise. The number of hours each individual exercised over the course of a week and their score on a standard cognitive test were recorded. Call the hours of exercise x and the score on the testy. The least-squares regression line for predictingyfrom x is f=64+5.2:: What does the number 64 represent in the equation? 0 a The avearge score on the test for all individuals. 0 b Predicted score on test when the individual exercises 5.2 hours per week. 0 c It's the yvintercept of the line, but it has no practical purpose in the context of the problem. 0 d Predicted score on test when the individual exercises 0 hours per week. The following scatter plot presents data on an individual's Body Mass Index and their percent of body fat. Scatterplot of %Fat vs BMI Based on the scatterplot, the least-squares line would predict that a person with a body mass index of 20 would have which of the following body fat percentage? 0 a 15% O b 24% O c 30% 0 d 18% The following scatter plot presents data on an individual's Body Mass Index and their percent of body fat. Scatterplot of %Fat vs BMI In the scatterplot, the point indicated by the open triangle 0 a has a positive value for the residual. O b has a negative value for the residual. O c has a zero value for the residual. 0 d does not have a residual. A study gathers data on the brain function of teenagers and routine exercise. The number of hours each individual exercised over the course of a week and their score on a standard cognitive test were recorded. Call the hours of exercise X and the score on the testy. The least-squares regression line for predictingy from x is =64+5.2x The standard deviation of the residuals for the data was found to be 0.85. What does this tell us? 0 a 85% of the variation in test scores is accounted for by the LSRL. O b The size of the typical prediction error from the LSRL is about 0.85. O c There is a strong, positive correlation between the variables. 0 d Each data point is 0.85 away from the LSRL. The time it takes to successfully navigate through a cornmaze was studied in relation to the amount of time the subjects were allowed to study the map before beginning. A computer regression analysis of time with the map (x in minutes) versus time to complete the maze (y in minutes) is shown below. Predictor Coef SE Coef T P Constant 129.092 5.996 21.53 0.000 Time -5.196 1.146 -4.54 0.001 s = 13.1089 RSq = 69.6% RSqtadj) = 66.2% The equation of the least-squares regression line is O a :129.0925.196x O b )'3=1.146+5.996x O c )'5=5.196+129.092x 0 d f=5.996+1_146)( The time it takes to successfully navigate through a cornmaze was studied in relation to the amount of time the subjects were allowed to study the map before beginning. A computer regression analysis of time with the map (x in minutes) versus time to complete the maze (y in minutes) is shown below. Predictor Coef SE: Coef T P Constant 129.092 5.996 21.53 0.000 Time -5.196 1.146 -4.54 0.001 s = 13.1089 99; = 69.6% RSq(adj) = 66.2% On average, how far are the predicted yvalues from the actualyvalues? O a 5.996 O b 0.696 O c 13.1089 0 d 1.146 1-..--.u\" .... '. r\"... .t, The time it takes to successfully navigate through a cornmaze was studied in relation to the amount of time the subjects were allowed to study the map before beginning. A computer regression analysis of time with the map (x in minutes) versus time to complete the maze (y in minutes) is shown below. Predictor Coef SE Coef T P Constant 129.092 5.996 21.53 0.000 Time -5.196 1.146 4.54 0.001 s = 13.1059 RSq = 59.5% R5q(adj] = 55.2% Which statement is an accurate interpretation for the data from the analysis? 0 a r = 0.834 proves a strong positive correlation O b 69.6% ofthe variation in minutes with the map can be accounted for by the linear regression. O c 69.6% ofthe variation in minutes to compelte the maze can be accounted for by the linear regression. Q d r = 0.696 proves a moderate positive correlation The time it takes to successfully navigate through a cornmaze was studied in relation to the amount of time the subjects were allowed to study the map before beginning. A computer regression analysis of time with the map (x in minutes) versus time to complete the maze (y in minutes) is shown below. Predictor Coef SE Coef T P Constant 129. 092 5.996 21.53 0. 000 Time -5. 196 1. 146 -4. 54 0. 001 S = 13. 1089 R-Sq = 69.68 R-Sq (adj ) = 66.28 Calculate and interpret the correlation coefficient. a r = -0.834 proves a strong negative correlation Ob r = 0.834 proves a strong positive correlation O c r = 0.696 proves a moderate positive correlation OThe average daily temperature (in degress Farenheit) and the number of visitors to a local beach during each week of the season are measured by a researcher. The goal is to determine if number of weekly visitors can be predicated based on the average daily temperature ofgiven week. Beach Visitors 600 525 450 375 300 225 I 50 75 Visitors 80 84 88 92 96 Average Daily Temperature (\"Fl Which of the following statements are supported by the scatterplot? |. There is a positive association between temperature and visitors. II. There is an high outlier in the plot. \"I. As the temperature increases, the number of visitors increases. 0 a I. ||,and Ill 0 b Ionly C I\" only 0 d land I\" Which of the following residual plots shows a data set for which a linear model would be the best fit? O a Ob O c 2 10 Od InderaidersThe average daily temperature (in degress Farenheit) and the number of visitors to a local beach during each week of the season are measured by a researcher. The goal is to determine if number of weekly visitors can be predicated based on the average daily temperature of given week. Beach Visitors 600 525 450 375 Visitors 300 225 150 75 0 80 84 88 92 96 Average Daily Temperature ("F) If the data point (86, 300) were removed from this study, how would the value of the correlation / change? O a r would be larger (closer to 1), because this point does not fall in the pattern of the rest of the data. Ob I would be larger (closer to 1), since you are eliminating one of the lower data points. O C would be smaller (closer to 0), because this point falls in the pattern of the rest of the data. O d r would be smaller (closer to 0), since there are fewer data points.A study is conducted to determine if one can predict the avearge daily temperature in January based on the location's latitude. The explanatory variable in this study is O a the avearge daily temperature. C) b month of the year. O c location's latitude. 0 d location's longitude. Two variables are said to be positively associated if 0 a smaller values of one variable are associated with larger values of the other. 0 b larger values of one variable are associated with smaller values of the other. smaller values of one variable are associated with both larger or smaller values of the other. O c 0 d larger values of one variable are associated with larger values of the other. In a statistics course a linear regression equation was computed to predict the obesity rate found in a given city based on the percent of people living below the poverty line in that same city. The equation of the least~squares regression line was f=12.1+0.56x where f represents the predicted obesity rate and X is the percent of people living below the poverty line. The obesity rate is the O a the response variable. 0 b the intercept. O c the slope. 0 d the explanatory variable. In a statistics course a linear regression equation was computed to predict the obesity rate found in a given city based on the percent of people living below the poverty line in that same city. The equation of the least~squares regression line was )7: 12.1 + 0.56x where )7 represents the predicted obesity rate and X is the percent of people living below the poverty line. Suppose a city has 9.5% of people living below the poverty level. What would be the predicted obesity rate? 0 a 19.? O b 5.3 O c 17.4 0 d 12.1 The correlation coefficient measures 0 a the strength and direction of the linear relationship between two quantitative variables. 0 b whether a cause and effect relation exists between two variables. 0 c whether or not a scatterplot shows an interesting pattern. 0 d the variation in the response variable that is accounted for in the LSRL. The coefficient of determination measures O the variation in the response variable that is accounted for in the LSRL. Ob whether a cause and effect relation exists between two variables. O the strength and direction of the linear relationship between two quantitative variables. C O d whether or not a scatterplot shows an interesting pattern