LESSON 8: Simple Linear Regression

Assignments

Read and study Chapter 11 in the textbook. Then solve exercise problems I through 10

For exercise problems 1 through 5, use the following pairs of values.

x 2 4 5 6 8 11 12

y -3 -1 -1 2 5 6 8

1. Find the equation for the regression of x on y.
2. Find the predicted value of y when x = 7.
3. Find a 95% confidence interval for the slope of the regression equation.
4. Find a 99% confidence interval for the mean of y given x = 10.
5. Calculate the coefficient of determination. Is there a strong relationship between x and y?

#6) The following table is similar to Table 11.3. It is used for making the preliminary computations for finding the least squares line

(e) Find the least squares line.

#7) Predicting sale prices of homes. Refer to the data on sale prices and total appraised values of 92 residential properties in art upscale Tampa, Florida, neighborhood, Exercise 11.18 (p. 606). A SAS simple linear regression printout for the analysis is given below:

(a) Specify Ho and Ha for testing whether there is positive linear relationship between appraised property value x and sale price y for residential properties sold in this neighborhood.

(c) Find a 95% confidence interval for the slope, \({{\beta }_{1}}\) on the printout. Interpret the result practically.

#8, #9 and #10) Consider the following pairs of measurements:

a. Construct a scattergram for these data.

b. Find the least squares line, and plot it on your scattergram.

c. Find s ² .

d. Find a 90% confidence interval for the mean value of y when x = 4. Plot the upper and lower bounds of the confidence interval on your scattergram.

e. Find a 90% prediction interval for a new value of y when x = 4. Plot the upper and lower bounds of the prediction interval on your scattergram.

f. Compare the widths of the intervals you constructed in parts d and e. Which is wider and why?

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