Sofia University Data Analysis 7 Exercise
Question 1
There are four problems. Use Excel to perform your computations and capture your answers and explanations. Be sure to check your math/formulas/functions carefully before uploading your Excel file.
1.Given are five observations for two variables, x and y.
|
xi |
1 |
2 |
3 |
4 |
5 |
|
yi |
3 |
7 |
5 |
11 |
14 |
- Develop a scatter diagram for these data.
- What does the scatter diagram you just developed indicate about the relationship between the two variables?
- Develop the estimated regression equation by computing the values of b0 and b1 using equations (14.6) and (14.7).
- Use the estimated regression equation to predict the value of y when x=4.
Upload your answers in an Excel file.
2. Given are five observations collected in a regression study on two variables.
|
xi |
2 |
6 |
9 |
13 |
20 |
|
yi |
7 |
18 |
9 |
26 |
23 |
- Develop a scatter diagram for these data.
- Develop the estimated regression equation for these data.
- Use the estimated regression equation to predict the value of y when x=6.
Upload your answers in an Excel file.
3. Given are five observations for two variables, x and y.
|
xi |
1 |
2 |
3 |
4 |
5 |
|
yi |
3 |
7 |
5 |
11 |
14 |
The estimated regression equation for these data is (hat{y}\)=0.20+2.60x=0.20+2.60x.
- Compute SSE, SST, and SSR using equations (14.8), (14.9), and (14.10).
- Compute the coefficient of determination r2r2. Comment on the goodness of fit.
- Compute the sample correlation coefficient.
Upload your answers in an Excel file.
4. Given are five observations for two variables, xx and yy.
|
xixi |
1 |
2 |
3 |
4 |
5 |
|
yiyi |
3 |
7 |
5 |
11 |
14 |
- Compute the mean square error using equation (14.15).
- Compute the standard error of the estimate using equation (14.16).
- Compute the estimated standard deviation of b1b1 using equation (14.18).
- Use the tt test to test the following hypotheses (α=0.05)(α=0.05):
H0: β1=0
Ha: β1≠0
- Use the FF test to test the hypotheses in part (D) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Upload your answers in an Excel file.
Textbook Readings
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Essentials of statistics for business and economics (9th ed.). Stamford, CT: Cengage.
- Chapter 14: Simple Linear Regression, Sections 14.1–14.5
- Appendix 14.4: Regression Analysis with Excel
Videos (7)
Note: The videos linked in this course will not play in the Canvas system. Clicking on the text links will take you to YouTube to watch the video.
Question 2
How does the range in
