Question

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	Monthly Salary ($)
2.7	3,500
3.4	3,800
3.7	4,200
3.2	3,700
3.5	4,200
2.7	2,500

The estimated regression equation for these data is  = -422.7 + 1,272.7x and MSE =137,386.

a. Develop a point estimate of the starting salary for a student with a GPA of 3.0 (to 1 decimal).
$

b. Develop a 95% confidence interval for the mean starting salary for all students with a 3.0 GPA (to 2 decimals).
$ (  ,  )

c. Develop a 95% prediction interval for Ryan Dailey, a student with a GPA of 3.0 (to 2 decimals).
$ (  ,  )

Answer 1

Gruen that- The data 9'uen in the ?uestion slalerneㆊ E anhelota, y- y a. 3500 75 0.95 3013.57 365.Ga 150 3.4 3800 0.2 0.04 3904.42 1041G0 50 30 る구 | 4200 | 0.5 215 0.35 42G. S 964 550 0 3G49-4 a506.0036 3700 50 3.5 | 4200 | О.З (G5 0.01 403530z. 06 550 0.a5 3013.59 263714.62 -1150 57 요구 、4500 S(-S) 549545. 2闩00 1120 451? 红一19.2 3.2. 거 100 2G50 rn Dim hegressiom 1272-7 0.88 (2-х) 64 -422-64

AeTess.on eluation i o Equation IS esimak of the starting slar -fa a sludent Pint sith GPn of 3.0 3.0 3395.4 Hence, poinlestimak of t starthing Salany a a sfudent artin 3395. 4 with GPA of 3.0 degrees of freedom de ะ 7-2-6-2 = 4 (fon-l-distribution table) Eritical value oP to.025 = 2.776 %, Confidence gntoval fa mean slating Salay k giuen b .05 거-요

95% CI- 3395.4 ±良み76 x 는 3325.4土2.7구G x 370. 6567 x / 01661+-0.04 0.88 (3395.4 ± 473.934 는 3325.4-473.934 , 339S. 4十473-934 95% 3869 . 334 292/.4GG L , he mean startin Salary C291.4, 386 33 5nterval:- 95% pediction y + to.cas ㄧ一 2 3.2 339S. 4さ2776 X | 549S45·4L G 5 (0-16) 0.04 는 3395 . 4 ± 27구Cx370·GS67 x | l to.1 2.77G X 320 -6567 x / l0078

(3395.4土113a, 845, (3395-4-иза. 845, 3395,4 t ll32.845) 95% PI -С дас 2.555) 4528-845 (2262-51,4529.25 95% prediction gnlerval fa Ryan dailey