In other words, the regression coefficient \beta_1 is not zero, and so there is a relationship between the dependent variable “job satisfaction” and the independent variable “hours of unpaid work per week.” This means that the independent variable “hours of unpaid work per week” is useful in predicting the dependent variable. This suggests that the assumption that the null hypothesis is true is most likely incorrect, and so the conclusion of the test is to reject the null hypothesis in favour of the alternative hypothesis. The p-value of 0.0082 is a small probability compared to the significance level, and so is unlikely to happen assuming the null hypothesis is true.This is the value calculated out by Excel in the regression summary table. Because the alternative hypothesis is a \neq, the p-value is the sum of the area in the tails of the t-distribution.The p -value for the tests on the regression coefficients are located in the bottom part of the table under the P-value column heading in the corresponding independent variable row.Here the subscript on \beta is 1 because the “hours of unpaid work per week” is defined as x_1 in the regression model. When conducting a test on a regression coefficient, make sure to use the correct subscript on \beta to correspond to how the independent variables were defined in the regression model and which independent variable is being tested.The alternative hypothesis is the claim that there is a relationship between the dependent variable and the independent variable “hours of unpaid work per week.” The alternative hypothesis is the claim that the regression coefficient for the independent variable x_1 is not zero.That is, the null hypothesis is the claim that there is no relationship between the dependent variable and the independent variable “hours of unpaid work per week.” The null hypothesis \beta_1=0 is the claim that the regression coefficient for the independent variable x_1 is zero.At the 5% significance level there is enough evidence to suggest that there is a relationship between the dependent variable “job satisfaction” and the independent variable “hours of unpaid work per week.” So the p-value=0.0082.īecause p-value=0.0082 \lt 0.05=\alpha, we reject the null hypothesis in favour of the alternative hypothesis. The p-value for the test on the hours of unpaid work per week regression coefficient is in the bottom part of the table under the P-value column of the Hours of Unpaid Work per Week row. The regression summary table generated by Excel is shown below: SUMMARY OUTPUT Previously, we learned that the population model for the multiple regression equation is Conduct and interpret a hypothesis test on individual regression coefficients.
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