- Economics 5 Name Ch 13 And 14 Practice Part 2 The Following Data Are The Monthly Salaries Y And The Grade Point Averages 1 (213.43 KiB) Viewed 25 times
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Economics 5 Name Ch 13 and 14 Practice Part 2 The following data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administration. GPA Salary уі yy (x-X) ..-y) (x-x) 9. y-y 09.-y2 e, y-y 6- y)2 6-y) Obser- vation index (i) 1 2 Xi 2.6 3.4 3.6 3.2 3.5 2.9 3300 3600 4000 3500 3900 3600 4 5 6 Totals SSR SSE TSS This is a continuation of the exercise for Chapter 13 in the previous Module. Use your answers to that exercise, or the Answer Key to that exercise, as a starting point. 1. Create an ANOVA table. Include a range for the p-value using the F statistic. The clearest instructions for how to do this are in the Learn part of Hawkes Lesson 14.5b. Because we are focusing on Simple Linear Regression in this course, the Number of Independent Variables (k) will be equal to 1. This means the Numerator Degrees of Freedom for the F statistic will also equal 1. Also, refer to sections 14.4 and 14.5 in the textbook (or eBook if you do not have a physical textbook) for another set of instructions on how to do this. The instructions are for Multiple Regression, but we will be doing this for Simple Linear Regression. The process is the same, except that in our case the number of independent variables is equal to one, so the Numerator Degrees of Freedom will always equal 1 and the Denominator Degrees of Freedom will always equal n - 2. Create a table similar to the lower part of Figure 14.7 on Page 799 in the textbook. You can create it manually using the formulas shown in the Formula box on Page 796 in the textbook. Note that df stands for Degrees of Freedom, SS stands for Sum of Squares, MS stands for Mean Square, F is the value of the F Statistics and Significance F means the p-value of the F statistic using the appropriate degrees of freedom. If you use a table to find the p-value you will not have an exact answer here, but instead you will have a range of possible values to compare to a. Also, note that "Residual” in Figure 14.7 refers to what is called the Error in SSE (Sum of Squared Errors) and MSE (Mean Squared Error).
For the next set of questions you will need to refer to Section 13.10 in the textbook or eBook. These are not covered in any Hawkes Learning or Khan Academy practice assignments. 2. Use the estimated regression equation to predict the salary for a student with a GPA of 3.0. This is Yp when Xp = 3.0. + 3. Calculate the estimated standard deviation for yp, known as Syp, when Xp = 3.0. The formula for Sy is Syp = se (xp-x)2 (x-x)2 See Question 12 in the first part of this Practice Assignment to find the value for Se and refer to the calculation table to find the value for (xi – x)2. 4. Find the value of ta/2,af, using a = .05. Remember that in Simple Linear Regression the df fort is n-2. 2 5. Calculate a 95% confidence interval for Elyp), the mean salary for all students with a GPA of 3.0. Use the format in interpretation 1 on Page 749 in the textbook. 6. Calculate the estimated standard deviation for the predicted salary for one particular student, John Chu, whose GPA is 3.0, known as Sind. The formula for Sind is: 1 (x - 2)2 Sind = Se 1 + n (x - 2)2
7. Develop a 95% prediction interval for the John Chu's salary. See the example on pages 750-751 of the textbook. 8. Compute the residuals for each observation and show the results in your table on page 1. This is the column labeled ei. 9. Construct a residual plot. 3 10. Do the regression assumptions about the error terms seem reasonable given the residual plot? Explain why or why not.