Question

In: Statistics and Probability

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

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.

Mean width: 7.647
Stdev width: 0.942
Mean height: 13.924
Stdev height: 1.703
Correlation coefficient: 0.7443

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

Solutions

Expert Solution

a) Height is considered as dependent variable y

Slope is

b) The Regression line to predict height is

c) Coefficient of Determination R2 = (0.7443)2 =0.554

55.4% of the variability variability in bean heights can be explained by the linear model of bean height vs width.

d) Width is considered as dependent variable y

Slope is

e) The Regression line to predict width is

orchestra answered 2 years ago
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