Q. 4.109 - 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 4.75 for High and Low temperatures in January for a random sample of 50 cities 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 0.9522.

(c) The percentage of variation in the observed values of the response variable explained by the regression is 95.22%.

(d) The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 95.22% which is greater than 50%. 

Part (a) Step 1. Given Information.

The data from Exercise 4.75 for High and Low temperatures in January for a random sample of 50 cities 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 Low and under X-variables enter a column of High.

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 Low.

3. In predictors, enter the column High.

4. Click OK.

Part (b) Step 2. The MINITAB output

The MINITAB output is: 

From the MINITAB output, the coefficient of determination is 0.9522.

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 95.22%.

Part (d) Step 1. Explanation.

The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 95.22% which is greater than 50%.