The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000) were recorded for nine different geographic regions.A 99% confidence interval for the slope of the regression line was determined to be (4.27,14.20) .Give an interpretation of this interval. Dependent variable is: Cancer Mortality Rate
R-squared = 85.8%
S = 14.00993 with 9 - 2 = 7 degrees of freedom $9.2314561.4187876.5065840.000332\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\\text { Constant } & 114.7156 & 8.045663 & 14.25807 & 0.00000198 \\\text { Index of Exp } & 9.231456 & 1.418787 & 6.506584 & 0.000332\end{array}$

A) Based on this regression,we are 99% confident that the mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
B) We can be 99% confident that with each unit increase in the index of exposure,the decrease in mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
C) We can be 99% confident that with each unit increase in the index of exposure,the increase in mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
D) Based on this regression,we are 99% confident that the mean cancer mortality rate is increasing between 4.27 and 14.20 deaths per 100,000 per year.
E) We are 99% confident that with each unit increase in the cancer mortality rate,the increase in the mean index of exposure is between 4.27 and 14.20 deaths per 100,000.

Question

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000) were recorded for nine different geographic regions.A 99% confidence interval for the slope of the regression line was determined to be (4.27,14.20) .Give an interpretation of this interval. Dependent variable is: Cancer Mortality Rate
R-squared = 85.8%
S = 14.00993 with 9 - 2 = 7 degrees of freedom

9.2314561.4187876.5065840.000332\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\\text { Constant } & 114.7156 & 8.045663 & 14.25807 & 0.00000198 \\\text { Index of Exp } & 9.231456 & 1.418787 & 6.506584 & 0.000332\end{array}

A) Based on this regression,we are 99% confident that the mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
B) We can be 99% confident that with each unit increase in the index of exposure,the decrease in mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
C) We can be 99% confident that with each unit increase in the index of exposure,the increase in mean cancer mortality rate is between 4.27 and 14.20 deaths per 100,000.
D) Based on this regression,we are 99% confident that the mean cancer mortality rate is increasing between 4.27 and 14.20 deaths per 100,000 per year.
E) We are 99% confident that with each unit increase in the cancer mortality rate,the increase in the mean index of exposure is between 4.27 and 14.20 deaths per 100,000.

suhara mazlan · Accepted Answer

Final Answer : C, Explanation :  The 99% confidence interval for the slope of the regression line indicates the range of the expected increase in the dependent variable (cancer mortality rate) for each unit increase in the independent variable (index of exposure). Since the interval is positive (4.27 to 14.20), it suggests an increase in cancer mortality rate with each unit increase in exposure.

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