Question

Name Economics 5 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. answer key -Edited a Search Obser- GPA index xyi (x,-司 Salaryxi-Xyv-V) 0.36 3301.3 -348.7 121558.2 1.8 122500 100.043766.2116.2 13505.216627626.4 2500 0.16 3882.4 232.4 54022.8 117.6 13823.2122500 0.0 -150.0 22498.8 22500 0.09 3824.3174.3 30387.5 75.7 5727.5 62500 210 2.6 3300 0.6 350 1.3 3.4 3600 02 -50 2 3 140 3.6 4000 0.4 350 0 3650.00.0 4 0 -150 3.5 3900 0.3 250 3.2 3500 0 75 6 2.9 36000.3-50 0.09 3475.7-174.3 30390.3124.3 15457.52500 430 85135.1 335000 SSE TSS 249863.9 Totals 19.2 21900 SSR 0.74 1. Create an ANOVA table. Include a range for the p-value using the F statistic. 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 p when xp -3.0 3. Callate the estimated standard deviation for , known as sy, when xp -3.0. The formula fors 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 -)2 Find the value of tzar using a-05. Remember that in Simple Linear Regression the df for tis n-2. 5. Calculate a 95% confidence interval for E(Y), 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 7, Develop a 95% prediction interval for the John Chu's salary. See the example on pages 750-751 of the textbook. Compute the residuals for each observation and show the results in your table on page 1. This is the column labeled e 8. 9. Construct a residual plot. 10. Do the regression assumptions about the error terms seem reasonable given the residual plot? Explain why or why not

Answer 1

1)

MS = SS/df

df Regression = k = 1

df Error = n--k-1 = 6-1-1 = 4

F = MS regression / MS Error

ANOVA
	df	SS	MS	F	Significance F
Regression	1	249864.8649	249864.8649	11.73968254	0.02662527
Residual	4	85135.13514	21283.78378
Total	5	335000

2)

y^ = a+ bx

Regression coefficient=β= 581.0811

Regression constant = α = 1790.5

y^ = 1790.5 + 581.0811 *x

= 1790.5 + 581.0811 *3

= 3533.7433

3)
s_y^ = se * sqrt(1/n + (xbar - xi)^2/Sxx))

se = sqrt(SSE/(n-2))
= 145.8896
xbar= 3.2
Sxx = 0.74

= 145.8896 * sqrt(1/6 + ( 3 - 3.2 )^2/0.74 )
= 68.5402819029
4)
t= t.inv.2t(0.05,4)
= 2.7764

5)
(y^ - t * s y^ , y^ - t * s y^)
=( 3533.7433 - 2.7764 * 68.5403 , 3533.7433 + 2.7764 * 68.5403)
=( 3343.448 , 3724.0386)