Using the Excel printout from Question 8, test the null hypothesis that there is
ID: 3227508 • Letter: U
Question
Using the Excel printout from Question 8, test the null hypothesis that there is no linear relationship between X and Y. Test at alpha = 0.05 significance level.
i. State the null hypothesis: _______________________
ii. State the alternate hypothesis: ___________________
iii. Test result and reason for test result __________________
iv. Assume that the null hypothesis is true. What is the probability of obtaining a test statistic equal to or more extreme than the one shown in the regression output?
Simple Linear Regression Analysis
Regression Statistics
Multiple R
0.6995
R Square
0.4892
Adjusted R Square
0.4609
Standard Error
8.7675
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
1325.3156
1325.3156
17.2413
0.0006
Residual
18
1383.6344
76.8686
Total
19
2708.9500
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95%
Upper 95%
Intercept
10.8698
16.7758
0.6479
0.5252
-24.3748
46.1144
-24.3748
46.11439
Runs Scored (X)
0.0972
0.0234
4.1523
0.0006
0.0480
0.1464
0.0480
0.14645
Calculations
b1, b0 Coefficients
0.0972
10.8698
b1, b0 Standard Error
0.0234
16.7758
R Square, Standard Error
0.4892
8.7675
F, Residual df
17.2413
18.0000
Regression SS, Residual SS
1325.3156
1383.6344
Confidence level
95%
t Critical Value
2.1009
Half Width b0
35.2446
Half Width b1
0.0492
Simple Linear Regression Analysis
Regression Statistics
Multiple R
0.6995
R Square
0.4892
Adjusted R Square
0.4609
Standard Error
8.7675
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
1325.3156
1325.3156
17.2413
0.0006
Residual
18
1383.6344
76.8686
Total
19
2708.9500
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95%
Upper 95%
Intercept
10.8698
16.7758
0.6479
0.5252
-24.3748
46.1144
-24.3748
46.11439
Runs Scored (X)
0.0972
0.0234
4.1523
0.0006
0.0480
0.1464
0.0480
0.14645
Explanation / Answer
null hypothesis: there is no significant linear realatioship between X and Y.
alternate hypothesis: there exist a significant linear realatioship between X and Y.
from above ANOVA test as p value is less then 0.05 level we reject null hypothesis and conclude that there exist a significant linear realatioship between X and Y.
probabilty of obtaining a test statistic equal to or more extreme than the one shown in the regression output=0.0006
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