Q. 4.108 - Elementary Statistics

Question

In Exercises 4.104 - 4.115, use the technology of your choice to perform the following tasks.

(a) Decide whether finding the regression line for the data is reasonable. If so, do parts (b) - (d).

(b) Obtain the coefficient of determination,

(c) Determine the percentage of variation in the observed values of the response variable explained by the regression and interpret your answer.

(d) State how useful the regression equation appears to be for making predictions.

The data from Exercise 4.74 for home size in (square feet) and assessed values (in thousands of dollars) for the same homes as in Exercis 4.107 are on the WeissStats site.

Step-by-Step Solution

Answer

(a) From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line.

(b) The coefficient of determination is 0.473.

(c) The percentage of variation in the observed values of the response variable explained by the regression is 47.3%.

(d) The regression equation is not useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 47.3% which is less than 50%. 

Part (a) Step 1. Given Information.

The data from Exercise 4.74 for home size in (square feet) and assessed values (in thousands of dollars) for the same homes as in Exercis 4.107 are on the WeissStats site.

Part (a) Step 2. The MINITAB procedure.

The MINITAB procedure for constructing scatterplot is:

1. Choose Graph > Scatterplot.

2. Choose with Connect Line, click OK.

3. Under Y-variables, enter a column of Value and under X-variables enter a column of Home size.

4. Click OK.

Part (a) Step 3. Graph the scatterplot.

The MINITAB output is:

From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line. 

Part (b) Step 1. The MINITAB procedure.

The MINITAB procedure for finding the coefficient of determination is:

1. Choose Stat > Regression > Regression.

2. In response, enter the column Value.

3. In predictors, enter the column Home Size.

4. Click OK.

Part (b) Step 2. The MINITAB output

The MINITAB output is: 

From the MINITAB output, the coefficient of determination is 0.473

Part (c) Step 1. Find the percentage of variation.

From the MINITAB output, the percentage of variation in the observed values of the response variable explained by the regression is 47.3%.

Part (d) Step 1. Explanation.

The regression equation is not useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 47.3% which is less than 50%.