# The US government is interested in understanding what predicts death rates. They have a set of data

The US government is interested in understanding what predicts death rates. They have a set of data that includes the number of deaths in each state, the number of deaths resulting from vehicle accidents (VEHICLE), the number of people dying from diabetes (DIABETES), the number of deaths related to the flu (FLU) and the number of homicide deaths (HOMICIDE).
Your run a regression to predict deaths and get the following output:
At alpha=0.05, what is indicated by the significance F in this problem?
A. The regression model does not significantly predict deaths.
B. The regression model significantly predicts deaths.
C. Two of the four independent variables significantly predict deaths.
D. Three of the four independent variables significantly predict deaths.

$\text{ANOVA}$

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Overall test:
Null hypothesis:
${H}_{0}$: There is no significant effect of the number of deaths from vehicle accidents, from diabetes, by flu, and due to homicide, on the death rates.
Alternative hypothesis:
${H}_{1}$: There is significant effect of the number of deaths from vehicle accidents, from diabetes, by flu and due to homicide, on the death rates.
Decision rule:
If p-value is less than or equal to level of significance, then reject the null hypothesis. Otherwise, failed or reject the null hypothesis.
The significance F indicates the p-value of the overall model, which is nearly 0 ($\approx$ 6.36772-14).
Thus, the probability of obtaining a test statistic value at least as extreme as the observed value of 37.43603514, when there is no significant effect of the number of deaths from vehicle accidents, from diabetes, by flu, and due to homicide, on the death rates, is approximately 0.
As p-value of 0 is less than 0.05, reject the null hypothesis.
Hence, there is enough evidence that there is significant effect of the number of deaths from vehicle accidents, from diabetes, by flu and due to homicide, on the death rates, at 0.05 level of significance.
Hence, correct answer is the regression model significantly predicts deaths.
However, using individual t test for each independent variable we can say which independent variable significantly predicts deaths.
Test for VEHICLE:
Null hypothesis:
${H}_{0}$: There is no significant effect of the number of deaths from vehicle accidents, on the death rates.
Alternative hypothesis:
${H}_{1}$: There is significant effect of the number of deaths from vehicle accidents, on the death rates.
The p-value for corresponding to VEHICLE is 0.06068593, which is greater than the p-value.
Thus, failed to reject the null hypothesis.
Hence, there is not enough evidence that there is significant effect of the number of deaths from vehicle accidents, on the death rates at 0.05 level of significance.
Test for DIABETES:
Null hypothesis:
${H}_{0}$: There is no significant effect of the number of deaths from diabetes, on the death rates.
Alternative hypothesis:
${H}_{1}$: There is significant effect of the number of deaths from diabetes, on the death rates.
The p-value for corresponding to DIABETES is nearly 0 (= 1.97533E-08), which is less than the p-value.
Thus, reject the null hypothesis.
Hence, there is enough evidence that there is significant effect of the number of deaths from diabetes, on the death rates at 0.05 level of significance.
Test for FLU:
Null hypothesis:
${H}_{0}$: There is no significant effect of the number of deaths to the FLU, on the death rates.
Alternative hypothesis:
${H}_{1}$: There is significant effect of the number of deaths to the FLU, on the death rates.
The p-value for corresponding to FLU is nearly 0 (= 2.9897E-07), which is less than the p-value.
Thus, reject the null hypothesis.
Hence, there is enough evidence that there is significant effect of the number of deaths to the FLU, on the death rates at 0.05 level of significance.
Test for HOMOCIDE:
Null hypothesis:
${H}_{0}$: There is no significant effect of the number of homicide deaths, on the death rates.
Alternative hypothesis:
${H}_{1}$: There is significant effect of the number of homicide deaths, on the death rates.
The p-value for corresponding to HOMOCIDE is 0.644470297 which is greater than the p-value.
Thus, fail to reject the null hypothesis.
Hence, there is not enough evidence that there is significant effect of the number of homicide deaths, on the death rates at 0.05 level of significance.
Hence, it can be said that two (VEHICILE and HOMICIDE) of the four independent variables significantly predict deaths.