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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: 7.439 Stdev width: 0.88 Mean height: 13.625 Stdev height: 1.825 Correlation coefficient: 0.7963

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

Solution:

Given:

Mean width: 7.439 Stdev width: 0.88

Mean height: 13.625 Stdev height: 1.825

Correlation coefficient: r = 0.7963

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

Let x = Width and y = Height

then Slope is:

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.

where

Thus

Part c) What fraction of the variability in bean heights can be explained by the linear model of bean height vs width?

Find r2

r2 = 0.79632

r2 =0.6341

Thus 0.6341 of the variability in bean heights can be explained by the linear model of bean height vs width.

Part 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.

Let x = Height and y = Width

then find slope:

Part 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.

where

Thus

orchestra answered 2 years ago
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