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ˆy=0.000402+132.45x ˆy=132.454.02x ˆx=132.45+0.000402ˆy ˆy=132.45+0.000402x Why

ID: 2923595 • Letter: #

Question

ˆy=0.000402+132.45x

ˆy=132.454.02x

ˆx=132.45+0.000402ˆy

ˆy=132.45+0.000402x



Why should we not use this regression line for prediction in this setting? Select the correct reasons below.

r2

is close to one.

The data is very scattered, the shape of the scatterplot is curved, not linear.

r2

is close to zero.

b

is close to zero.



What is r2?

Give your answer to 3 decimal places.

What does this value say about the success of the regression line in predicting yield?

r2

is close to zero, and therefore the regression line will give an accurate prediction of yield.

r2

is close to zero, and therefore the regression line will give a poor prediction of yield.

r2

is close to one, and therefore the regression line will give a poor prediction of yield.

r2

is close to one, and therefore the regression line will give an accurate prediction of yield.



First, calculate the mean ¯x of the data set.
Round to 1 decimal place.

Next calculate the mean ¯y.
Round to 2 decimal places.

Now use the regression equation exactly as given in the first part of this problem, and find the predicted value for y when x = ¯x. (Substitute ¯x into the least-squares line to find y).
Round to 2 decimal places.

Plants per acre 12,000 16,000 Yield (bushels per acre) 150.1 113.0 118.4 142.6 166.9 120.7 135.2 149.8 24,00134.7 130.4 156.1 149.9 134.7 138.4 156.1 119.0 150.5 28,000

Explanation / Answer

Answer:

Use your calculator to construct a scatterplot of this data (Note: your data list should have 17 values). Find the least-squares regression line for predicting yield from planting rate and add this line to your plot. The equation for this line is:

ˆy=0.000402+132.45x

ˆy=132.454.02x

ˆx=132.45+0.000402ˆy

Answer: ˆy=132.45+0.000402x



Why should we not use this regression line for prediction in this setting? Select the correct reasons below.

r2 is close to one.

Answer: The data is very scattered, the shape of the scatterplot is curved, not linear.

r2 is close to zero.

B is close to zero.



What is r2?
r2 =0.018
Give your answer to 3 decimal places.

What does this value say about the success of the regression line in predicting yield?

r2 is close to zero, and therefore the regression line will give an accurate prediction of yield.

Answer: r2 is close to zero, and therefore the regression line will give a poor prediction of yield.

r2 is close to one, and therefore the regression line will give a poor prediction of yield.

r2 is close to one, and therefore the regression line will give an accurate prediction of yield.



First, calculate the mean ¯x of the data set.

18,823.5


Round to 1 decimal place.

Next calculate the mean ¯y.

140.02


Round to 2 decimal places.

Now use the regression equation exactly as given in the first part of this problem, and find the predicted value for y when x = ¯x. (Substitute ¯x into the least-squares line to find y).
Round to 2 decimal places.

Predicted y =132.45+0.000402*18823.5

=140.017047

=140.12 ( two decimals).