Question

The data shown below for the dependent​ variable, y, and the independent​ variable, x, have been collected using simple random sampling.

x   y
11   100
13   80
15   80
12   90
20   60
17   60
15   70
13   90
15   90
17   80

a. Complete the linear regression equation below Round to one decimal place as needed.) b. Calculate the sum of the squared residuals. SSE-L (Round to the nearest whole number as needed) What is the total sum of squares? SSTRound to the nearest whole number as needed.) Determine the coefficient of determination RRound to two decimal places as needed) c What is the standard error of the estimate? SRound to two decimal places as needed.) d. Determine the standard error for the regression slope S,Round to two decimal places as needed.) e. What are the appropriate hypotheses to test? C. Hop,#0 HA: β1 > 0 HA ,20 Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice. Round to four decimal places as needed) Calculate the simple linear regression test statistict tRound to four decimal places as needed) Since the test statistic in the rejection region, the null hypothesis. Conclude that the regression modelsignificant. This means that knowing x useful help in predicting y

Answer 1

X	Y	XY	X²	Y²
11	100	1100	121	10000
13	80	1040	169	6400
15	80	1200	225	6400
12	90	1080	144	8100
20	60	1200	400	3600
17	60	1020	289	3600
15	70	1050	225	4900
13	90	1170	169	8100
15	90	1350	225	8100
17	80	1360	289	6400

Sample size, n =	10
Ʃ x =	148
Ʃ y =	800
Ʃ xy =	11570
Ʃ x² =	2256
Ʃ y² =	65600
x̅ =	14.8
y̅ =	80
SSxx = Ʃx² - (Ʃx)²/n =	65.6
SSyy = Ʃy² - (Ʃy)²/n =	1600
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	-270

a) Regression equation:

Slo[e, b = SSxy/SSxx =	-4.115854
Intercept, a = y̅ -b* x̅ =	140.91463

ŷ = 140.9 - 4.1 x

b) SSE, SST, R²

SSE = SSyy -b*SSxy =	488.7195 = 489
SST = SSyy = Ʃy² - (Ʃy)²/n =	1600
R2 = 1- SSE/SST	0.69

c) Standard error of estimate =

se = √(SSE/(n-2)) =

7.82

d) Standard error for regression slope =

sb1 = se/√SSxx =

0.97

e) Null and Alternative hypothesis: Answer F

Ho:   β₁ =   0
H1:   β₁ ╪   0

Critical value:

At α = 0.05 and df = n-2 = 8, critical value, t_c = T.INV.2T(0.05, 8) = 2.3060

Rejection Region:

Answer C: t < -2.3060 or t < 2.3060

Test statistic:

t =

b /sb1 =

-4.2651

The test statistic is in the rejection region. Reject the null hypothesis.