7-2 Discussion Interpreting Multiple Regression Models
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Jan 9, 2024
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7-2 Discussion: Interpreting Multiple Regression Models
1.
Is at least one of the two variables (weight and horsepower) significant in the model? Run the overall F-test and provide your interpretation at 5% level of significance. See Step 5 in the Python script. Include the following in your analysis:
a.
Define the null and alternative hypothesis in mathematical terms and in words.
H
0
: β
1 = β
2
= 0
H
a
: at least one β
n
≠ 0 for n = 1, 2.
The null hypothesis states that there is not a statistical significance between variables. The alternative hypothesis states that there is a statistical significance
between the variables. b.
Report the level of significance.
The level of significance is 0.05. c.
Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-
Statistic) in the output).
The test static is 66.68 and the P-value is 3.59e
-11
. d.
Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?
The null hypothesis should be rejected because the P-value of 3.59e
-11
is less than the level of significance at 0.05. This will tell us that a significant relationship exists between the variables. 2.
What is the slope coefficient for the weight variable? Is this coefficient significant at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.
The slope coefficient for the weight variable is -3.8409. The coefficient is significant because the P-value of 0.000 is less than the significance level at 0.05. 3.
What is the slope coefficient for the horsepower variable? Is this coefficient significant
at 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.
The slope coefficient for horsepower is -0.0322. The coefficient is significant because the P-value of 0.001 is less than the significance level at 0.05.
4.
What is the purpose of performing individual t-tests after carrying out the overall F-
test? What are the differences in the interpretation of the two tests?
F-test determine whether a relationship exist with at least one predictor variable. So after we check if any linear relationship exist, we conduct a t-test to determine whether
a single variable has an effect. 5.
What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic.
The coefficient of determination for multiple regression model is 0.832. The value for R
2 means that 83.2% of the data fits the regression model. 83.2% of the total variation in miles per gallon is accounted for by the regression model with horsepower and weight as predictors.
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