Question

Below are the values for two variables x and y obtained from a sample of size 5. We want to build a regression equation based the sample data.

ŷ = b₀ + b₁x

y	x
16	5
21	10
8	6
28	12
53	14

11	On average the observed y deviate from the predicted y by,
a	10.73
b	10.04
c	9.53
d	8.76

12	Sum of squares total (SST) is,
a	1096.3
b	1178.8
c	1296.7
d	1361.5

13	Sum of squares regression (SSR) is,
a	906.06
b	983.56
c	1008.47
d	1065.20

14	The fraction of variations in y explained by x is:
a	0.5534
b	0.6149
c	0.7686
d	0.8455

15	The x and y data are sample data from the population of X and Y to compute b₁ as an estimate of the population slope parameter β₁. The sample statistic b₁ is the estimator of the population parameter β₁. The estimated measure of dispersion of the sample statistic b₁ is,
a	0.929
b	1.239
c	1.549
d	1.936

16	The margin of error for a 95% confidence interval for β₁ is,
a	4.77
b	4.34
c	3.94
d	2.96

17	To perform a hypothesis test with the null hypothesis H₀: β₁ = 0, we need a test statistic. The test statistic for this hypothesis test is,
a	1.741
b	2.123
c	2.589
d	3.157

Answer 1

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Answer:

11)

9.53

12)

1178.8

13)

906.06

14)

0.7686

15)

1.239

16)

confidence interval for slope                  
α=   0.05              
t critical value=   t α/2 =    3.182   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    9.53491   /√   59.20   =   1.239

margin of error ,E= t*std error =    3.182   *   1.239   =   3.94

17)

t stat = estimated slope/std error =ß1 /Se(ß1) =    3.9122   /   1.2392   =   3.157