Directions: Submit your final answers to D2L Quizzes before the due date/time.

1. Consider the following data for two abstract variables, x and y. Column i is an ID variable.

i

1 135 145

2 110 100

3 130 120

4 145 120

5 175 130

6 160 130

7 120 120

Use Microsoft Excel’s Data Analysis Tool Pak to calculate the descriptive statistics for both variables.

(a) What is the mean of x?

(b) What is the mean of y?

Use Microsoft Excel’s Data Analysis Tool Pak to fit a regression equation using y as the dependent variable.

(c) What is ?

(d) What is ?

(e) What is ?

(f) What is SST?

(g) What is SSE?

(h) What is SSR?

(i) What is MSE?

(j) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(k) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(l) What is the correlation coefficient for these 2 variables?

(m) Does your model pass the F-test for the whole regression?

Perform a residual analysis for your regression. Specifically, create 2 scatterplots. The first should have x as the horizontal axis and the residuals (errors) as the vertical axis. The second should have x as the horizontal axis and the standardized residuals (errors) as the vertical axis. Round your 2 residual columns to 4 decimal places.

(n) Did your regression pass the residual analysis?

2. Consider the following data for two abstract variables, x and y. Column i is an ID variable.

i

1 4 12

2 5 14

3 7 16

4 8 15

5 10 18

6 12 20

7 12 24

8 22 19

Use Microsoft Excel’s Data Analysis Tool Pak to calculate the descriptive statistics for both variables.

(a) What is the mean of x?

(b) What is the mean of y?

Use Microsoft Excel’s Data Analysis Tool Pak to fit a regression equation using y as the dependent variable.

(c) What is ?

(d) What is ?

(e) What is ?

(f) What is SST?

(g) What is SSE?

(h) What is SSR?

(i) What is MSE?

(j) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(k) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(l) What is the correlation coefficient for these 2 variables?

(m) Does your model pass the F-test for the whole regression?

Perform a residual analysis for your regression. Specifically, create 2 scatterplots. The first should have x as the horizontal axis and the residuals (errors) as the vertical axis. The second should have x as the horizontal axis and the standardized residuals (errors) as the vertical axis. Round your 2 residual columns to 4 decimal places.

(n) Did your regression pass the residual analysis (Yes or No)?

Test your data for outliers. [Hint: There is one outlier.]

(o) Which observation (which i) was the outlier?

Re-estimate the regression without the outlier.

(p) What is now?

(q) What is now?

(r) What is now?

(s) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant now?

(t) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant now?

(u) What is the correlation coefficient for these 2 variables now?

(v) Does your new model pass the F-test for the whole regression?

3. Consider the following data on a sample of nations. You know their gold holdings and debt.

Country Gold value

($ billion) Debt

(% of

GDP)

China 63 17.7

France 146 81.7

Germany 203 83.2

Indonesia 33 69.2

Italy 147 119.0

The Netherlands 36 63.7

Russia 50 9.9

Switzerland 62 55.0

United States 487 93.2

Use Microsoft Excel’s Data Analysis Tool Pak to calculate the descriptive statistics for both variables.

(a) What is the mean gold value?

(b) What is mean debt?

Use Excel’s Data Analysis Tool Pak to fit a regression equation using Debt as the dependent variable.

(c) What is ?

(d) What is ?

(e) What is ?

(f) What is SST?

(g) What is SSE?

(h) What is SSR?

(i) What is MSE?

(j) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(k) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant?

(l) What is the correlation coefficient for these 2 variables?

(m) Does your model pass the F-test for the whole regression?

Perform a residual analysis for your regression. Specifically, create 2 scatterplots. The first should have gold value as the horizontal axis and the residuals (errors) as the vertical axis. The second should have gold value as the horizontal axis and the standardized residuals (errors) as the vertical axis. Round your 2 residual columns to 4 decimal places.

(n) Did your regression pass the residual analysis (Yes or No)?

Test your data for outliers. [Hint: There is one outlier.]

(o) Which observation (which country) was the outlier?

Re-estimate the regression without the outlier.

(p) What is now?

(q) What is now?

(r) What is now?

(s) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant now?

(t) At what confidence level (not significant, 90%, 95%, or 99%) is statistically significant now?

(u) What is the correlation coefficient for these 2 variables now?

(v) Does your new model pass the F-test for the whole regression?

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