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AP Statistics3.2 Part 2 Homework WorksheetLSRL and r2Please show all work on a separate piece of paperThe mean height of American women in their early twenties is about 64.5 inches and the standard deviation is about 2.5 inches. The mean height of men the same age is about 68.5 inches, with standard deviation about 2.7 inches, lastly, the correlation between the heights of husbands and wives is about r = 0.5. What is the equation of the regression line of the husband’s height based on the wife’s height in young couples? Draw a graph of this regression line. Predict the height of the husband of a woman who is 67 inches tall.Based on the information from Number 1:Find r2 and interpret this value in context. Complete sentence!Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. Here is the data:Mass:36.154.648.542.050.642.040.333.142.434.551.141.2Rate:9951425139614181502125611899131124105213471204Enter the data into your calculator and make a scatterplotUse your calculator regression function to find the equation of the least-squares regression line. Add this line to your scatterplot from (a)Explain in words what the slope of the regression line tells us.Another woman has a lean body mass of 45 kilograms. What is her predicted metabolic rate?Looking at your graph and regression line, which point has the largest residual? Explain what the value of the residual means in context. For your regression line performed earlier, what is the r2 value? Explain what this means in this setting. 3855720000The figure to the right is a scatterplot of reading test scores against IQ test scores for 14 fifth-grade children. The line is the least-squares regression line for predicting the reading score from IQ score. If another child in this class has IQ score 110, you predict the reading score to be close to 50b. 60c.70d.80e. 90The slope of the line in the figure is closest to a. -1b. 0c. 1d. 2e. 46For problems 6-10 refer to the following:Measurements on young children in Mumbai, India, found this least-squares regression line for predicting height y from arm span x:y=6.4+0.93x.Measurements are in centimeters.How much does height increase on average for each additional centimeter of arm span?0.93 cmd. 6.4 cm1.08 cme. 7.33 cm5.81 cmAccording to the regression line, the predicted height of a child with an arm span of 100 cm is about106.4 cm 99.4 cmd. 15.7 cm93 cm7.33 cmBy looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span isgreater than zeroless than zero0.936.4Can’t tell without seeing the dataIn addition to the regression line, the report on the Mumbai measurements says that r2 = 0.95. This suggests thatAlthough arm span and height are correlated, arm span does not predict height very accurately.Height increases by 0.95=0.97 cm for each additional centimeter of arm span.95% of the relationship between height and arm span is accounted for by the regression line.95% of the variation in height is accounted for by the regression line.95% of the height measurements are accounted for by the regression line.One child in the Mumbai study had height 59 cm and arm span 60 cm. This child’s residual is-3.2 cm-2.2 cm-1.3 cm3.2 cm62.2 cm ................
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