Question

Name Economics 5 Ch 13 Practice The follo wing data are the monthly salaries y and the grade point averages x for students who obtained a bachelor's degree in business administ ration Obser vation index xi 2.6 3300 3.4 3600 3.6 4000 3.2 3500 3.5 3900 2.9 3600 TSS Totals SSR SSE 1. Calculate and y 2. Use the least squares method to develop the estimated regression equation. Use two decimal points in your answers for bo and bi. 3. Calculate the values of for each x in the data. Show the answers in the table 4. Compute the Sum of Squares Due to Regression, known as SSR. 5. Compute the Sum of Squares Due to Error, known as SSE. 6. Compute the Total Sum of Squares, known as TSS (or SST) 7. Compute r 8. What is the value of the sample correlation coefficient? 9. Is the relationship between GPA and salary positive or negative? 10. Based on your regression analysis, how much does predicted salary change whern GPA increases by 1.0?

Answer 1

x	y	x-xbar	y-ybar	(x-xbar)(y-ybar)	(x-xbar)^2	y^	(y^ - ybar)	(y^ - ybar)^2	ei	(yi - y^)^2	(yi-ybar)^2
2.6	3300	-0.6	-350	210	0.36	3301.351	-348.649	121555.9	-1.35135	1.82615	122500
3.4	3600	0.2	-50	-10	0.04	3766.216	116.2162	13506.21	-166.216	27627.83	2500
3.6	4000	0.4	350	140	0.16	3882.432	232.4324	54024.84	117.5676	13822.13	122500
3.2	3500	0	-150	0	0	3650	0	0	-150	22500	22500
3.5	3900	0.3	250	75	0.09	3824.324	174.3243	30388.97	75.67568	5726.808	62500
2.9	3600	-0.3	-50	15	0.09	3475.676	-174.324	30388.97	124.3243	15456.54	2500
3.2	3650			430	0.74			249864.9		85135.14	335000

1)xbar = 3.2
ybar = 3650

2)
slope = sum ((x-xbar)(y-ybar)) / sum (x-xbar)^2
= 430/0.74
= 581.0811

b0 = ybar - slope*xbar
= 1790.541

3) See in the table
4)
SSR = 249864.9
5)
SSE = 85135.14
6)
SST = 335000

7)
r^2 = SSR/SST =
8)
r = 0.8636
9)
there is positive relationship

10)this is slope
= 581.0811

11)

MSE = sqrt(SSE/(n-2)) = 21283.78

12)s = sqrt(MSE) = 145.8896
13)sb1 = sqrt(MSE/SSx)
= 169.5932

14)
t = 3.4263
15)
df = 4
16)
p-value = 0.0266

0 < p-value < 0.05

17)

p-value < alpha
hence we reject the null hypothesis

we conclude that there is statistically significant relationship

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