3. A study examined the relationship between the sepal length and sepal width for two varieties of an exout Varieties X and O are represented by x's and o's, respectively, in the following scatterplot. Which of the following statements is true? 2.0 Worldisseat blaft A 15 dyord norw sas art 1.0 5982 29 andif elem Of 0.5 * * * * 0.0 10 12 16 width A. Considering Variety X only, there is a positive correlation between sepal length and width. B. Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope. C. Considering both varieties together, there is a negative correlation between sepal length and width. D. Considering each variety separately, there is a negative correlation between sepal length and width. E . Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope. 4. A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. 74 pelemet not sprisbivs 72 70+ 68- A Arm Span 66+ 64- Fig 62 60. les li saimaish of sieb serge wna srizu 65 70 75 Height If the point labeled A is removed, which of the following statements would be true? A. The slope of the least squares regression line is unchanged and the correlation coefficient increases. B. The slope of the least squares regression line is unchanged and the correlation coefficient decreases. C. The slope of the least squares regression line increases and the correlation coefficient increases. 101 D. The slope of the least squares regression line increases and the correlation coefficient decreases. E . The slope of the least squares regression line decreases and the correlation coefficient increases.it answers on answer sheet. 11. Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-squares regression line produced from a random sample is milk = 40.8 - 1.1(age) with 12 = 0.36 Based on the model: (3 pts each) A. Determine the value of the correlation coefficient. B. Predict a cow's production at age 4. C. A certain cow is 8 years old and the residual was 5 gallons. What was the cow's actual production? D. Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years? BONUS (+2): COMPLETE LAST! MAKE SURE YOU HAVE TIME TO FINISH! Students expose marine bacteria to X-rays for time periods from 1 to 15 minutes. They record the number of surviving bacteria (in s) on a culture plate after each exposure time. A logarithmic regression is the best fit for this data with the least squares given below. surviving bacteria = 329 - 121 . In(time exposed) BONUS (+2): The actual number of surviving bacteria (in hundreds) for a time t is 106. Its residual is -6.2. Find the amount of time this bacteria was exposed to X-rays.8. A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat gave the following results: Predicted Calories = 97.1053 + 9.6525(Fat). Which of the following is false? A. It is estimated that for every additional gram of fat in the cereal, the number of calories increases by about 10. B. It is estimated that in cereals with no fat, the total amount of calories is about 97. C. If a cereal has 2 g of fat, then it is estimated that the total number of calories is about 116. . The correlation between amount of fat and calories is positive. E . If one cereal has 140 calories and 5 g of fat, its residual is about 5 calories. 9. Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale? 1 sausond BY A. . -1 8 B. -0.75 Hasrito C. 0 D. 0.75 E . 1 10. Data were collected on the fiber diameter and the fleece weight of wool taken from a sample of 20 sheep. The data are shown in the following graphs. Graph 1 is a scatterplot of fleece weight versus fiber diameter with the respective least-squares regression line shown. Graph 2 is the associated plot of the residuals versus the predicted values. Graph 1 Graph 2 E 4- 15+ 10 Residual Fleece Weight Fleece Weight h D -4 C 20 25 30 35 40 8 9 10 11 12 13 14 15 Fiber Diameter Predicted Fleece Weight One point is circled on graph 1. Five points labeled A, B, C, D, and E are identified on graph 2. Which point on graph 2 represents the residual for the circled point on graph 1? A. A B. B C. C D. D E . F5. Consider n pairs of numbers (X1, Y1), (X2, Yz), ..., and (X,, yn). The mean and standard deviation of the x-values are x =5 and sy = 4, respectively. The mean and standard deviation of the y-values are y = 10 and sy = 10 respectively. Of the following, which could be the least squares regression line? A. y = -5.0 + 3.0x B. V = 3.0x C. y = 5.0 + 2.5x D. y = 8.5 + 0.3x E. y = 10.0 + 0.4x 6. A researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age. 0.6- A. Yes, because there is a clear pattern displayed in the 0.4- residual plot. 0.2- B. Yes, because about half the residuals are positive and the Residuals other half are negative. 0.0- C. Yes, because as age increases, the residuals increase. -0.2- D. No, because the points appear to be randomly distributed. -0.4- . No, because the graph displays a U -shaped pattern. -0.6- 3 Age in Years 7. An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses-0.0, 0.5, 1.0, 1.5, 2.0-in milligrams (mg) of medication. The results are shown in the scatterplot below. 14T 12- 10- Pain Relief (hours) . . . A N 0.0 0.5 1.0 1.5 2.0 Dose (mg) The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose? A. The sum of the residuals is less than 0. B. The sum of the residuals is greater than 0. C. There are outliers associated with the lower doses. D. The variation in the hours of pain relief is not the same across the doses. E. There is a positive linear relationship between the residuals and the dose