The accompanying table shows the regression results when estimating y = 0 + 1 x
ID: 3223396 • Letter: T
Question
The accompanying table shows the regression results when estimating y = 0 + 1x + .
df
SS
MS
F
Significance F
Regression
1
78.5900
78.5900
15.82
0.0106
Residual
5
24.8385
4.9677
Total
6
103.4286
Coefficients
Standard Error
t-stat
p-value
Intercept
15.6615
2.4020
6.520
0.0013
x
1.6927
0.4256
3.977
0.0106
a. Specify the competing hypotheses to determine whether x is significant in y.
b. At the 5% significance level, is x significant? Explain.
df
SS
MS
F
Significance F
Regression
1
78.5900
78.5900
15.82
0.0106
Residual
5
24.8385
4.9677
Total
6
103.4286
Coefficients
Standard Error
t-stat
p-value
Intercept
15.6615
2.4020
6.520
0.0013
x
1.6927
0.4256
3.977
0.0106
Explanation / Answer
a. Null Hypothesis : Ho : there is not a significant linear relationship between the independent variable X and the dependent variable Y and B1= 0
H1: there is a significant linear relationship between the independent variable X and the dependent variable Y and B1 0
b. Test Statistic :
t = b1 / SE = -1.6927/ 0.4256 = - 3.977
for alpha = 0.05 significance level tcritical = 2.571
where t > tcriticalso null hypothesis is wrong and we can reject it and can say that there is a significant linear relationship between the independent variable X and the dependent variable Y and b1 0
We can also conclude that by checking respective p - value which is equal to 0.0106 < p = 0.05 .
So x is significant in y and linear relationship between two variables are significant.
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