Question

The index of exposure to radioactive waste, x, and the cancer mortality rates, y, (deaths per 100,000) were recorded for nine different Oregon counties. Use the regression analysis provided below to perform the hypothesis test to determine if the index of exposure is useful as a predictor of cancer mortality rate. The regression equation is = 114.7156 + 9.231456x R-sq = 85.8% 9- 2 = 7 degrees of freedom Predictor Coef Constant 114.7156 Index of Exp 9.231456 SE(Coef) I 8.045663 1425807 1.418787 6.506584 P 0.00000198 0.000332 Ho: No linear relationship between the index of exposure and cancer mortality rate, ß = 0. Ha: There is a linear relationship between the index of exposure and cancer mortality rate, B+ 0. State your conclusion assuming a = 0.05. Since the P-value = 0.000332 <0.05, we reject Ho and conclude that there is no linear relationship between the index of exposure and cancer mortality. Since the P-value = 0.000332 <0.05, we reject Ho and conclude that there is a linear relationship between the index of exposure and cancer mortality. Since the P-value = 0.00000198 < 0.05, we reject Ho and conclude that there is no linear relationship between the index of exposure and cancer mortality. Since the P-value = 0.00000198 < 0.05, we reject Ho and conclude that there is a linear relationship between the index of exposure and cancer mortality. O No conclusions can be drawn without a chi-squared test of independence.

Answer 1

To test the significance of Linear regression model, it is good to see the value of either R² or p-value. We know that in any hypothesis problem, if the p-value is less than the size of the test, then we reject the Null hypothesis.

To test the significant relationship between two variable in a regression model, we see the p-value of the independent variable and ignore the p-value of the constant term. Here, P-value of Independent term (Index of Exposure) is 0.000332<α=0.05, so we can conclude that the slope is not zero, which in turn suggests that changes in the predictor variable are associated with changes in the response variable. Thus, we can conclude

(b) Since p-value=0.000332 <0.05, we reject H0 and conclude that there is a linear relationship between the index of exposure & cancer mortality.