Given are five observations for two variables, x and y. a. Develop the regressio
ID: 3273440 • Letter: G
Question
Given are five observations for two variables, x and y. a. Develop the regression equation by computing the values of beta_0 and beta_1. b. Use the estimated regression equation to predict the value of y when x = 6. c. Compute SSE, SST, and SSR. d. Compute the coefficient of determination r^2. Comment on the goodness of fit. e. Compute the sample correlation coefficient. f. Compute the mean square error (MSE). g. Compute the standard error of the estimate. h. Compute the estimated standard deviation of beta_1. i. Use the t-test to test the following hypotheses at the 5% significance level: H_0: beta_1 = 0 H_1: beta_1 notequalto 0 Is beta_1 significant at the 5% level? j. Construct a 99% confidence interval for beta_1.Explanation / Answer
Answer:
a).
0=30.3312 1= -1.8766
b).
the estimated regression line is y=30.3312 -1.8766*x
when x=6, predicted y=30.3312 -1.8766*6
=19.0716
c).
SSE=6.3312
SST=114.80
SSR =108.4688
d).
R square = 0.945
94.5% of variation in y is explained by x.
e).
correlation coefficient r= -0.972
f).
MSE=2.1104
g).
standard error =1.453
h).
standard error of 1 =0.2618
i).
t=-1.8766/0.2618
= -7.169
Table value of t with 3 DF at 0.05 level =3.18
Reject Ho if calculated t < -3.18 or t>3.18
Calculated t = -7.169 falls in the rejection region.
The null hypothesis is rejected.
1 is significant at 5% level.
j).
99% CI for 1 = (-3.4055, -0.3477).
Regression Analysis
r²
0.945
n
5
r
-0.972
k
1
Std. Error
1.453
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
108.4688
1
108.4688
51.40
.0056
Residual
6.3312
3
2.1104
Total
114.8000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
99% lower
99% upper
Intercept
30.3312
1.1881
25.530
.0001
23.3918
37.2705
x
-1.8766
0.2618
-7.169
.0056
-3.4055
-0.3477
Regression Analysis
r²
0.945
n
5
r
-0.972
k
1
Std. Error
1.453
Dep. Var.
y
ANOVA table
Source
SS
df
MS
F
p-value
Regression
108.4688
1
108.4688
51.40
.0056
Residual
6.3312
3
2.1104
Total
114.8000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
99% lower
99% upper
Intercept
30.3312
1.1881
25.530
.0001
23.3918
37.2705
x
-1.8766
0.2618
-7.169
.0056
-3.4055
-0.3477
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