A group of students measure the length and width of a random sample of beans. Th

Question

A group of students measure the length and width of a random sample of beans. They are interested in investigating the relationship between the length and width. Their summary statistics are displayed in the table below. All units, if applicable, are millimeters.

a) The students are interested in using the width of the beans to predict the height. Calculate the slope of the regression equation.

b) Write the equation of the best-fit line that can be used to predict bean heights. Use x to represent width and y to represent height.    

c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width? Express your answer as a decimal.

d) If, instead, the students are interested in using the height of the beans to predict the width, calculate the slope of this new regression equation.

e) Write the equation of the best-fit line that can be used to predict bean widths. Use x to represent height and y to represent width.    

Mean width: 7.586 Stdev width: 0.873 Mean height: 14.603 Stdev height: 1.632 Correlation coefficient: 0.8651

Explanation / Answer

a)slope =r*Sy/Sx=0.8651*1.632/0.873=1.6172

b) intercept =(ybar-slope*xbar)=14.603-1.617*7.586=2.336

hence equation of the best-fit line:Yhat=2.336+1.617*x

c)

fraction of the variability =r2 =(0.8651)2 =0.7484

d)

slope =0.8651*0.873/1.632=0.463

e)

intercept =(ybar-slope*xbar)=7.586-14.603*0.463=0.825

equation of the best-fit line:Yhat =0.825+0.463x

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