Week 7 discussion mat 243

Content type

User Generated

Uploaded By

oerhnuuq

Pages

Rating

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.

H0: β1 = β2 = 0

Ha: at least one βn ≠ 0 for n = 1, 2.

Ho: The regression model is not significant.

H1: The regression model is significant

b. Report the level of significance.

level of significance α = 0.05

c. Include the test statistic and the P-value. (Hint: F-Statistic and Prob (F-Statistic)

in the output).

F-Statistic: 60.99

Prob (F-Statistic) or P-Value: 9.69e-11

d. Provide your conclusion and interpretation of the test. Should the null hypothesis

be rejected? Why or why not?

Because the P-value is lesser than the level of significance, the null hypothesis

is rejected. A significant linear relationship exists between Y and the set {X1,

X2} when X1= wt(weight)and X2 = hp(horsepower).

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.

-3.8679

The P-value is less than the significance level of 0.05, therefore it is statistically

significant.

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.

-0.0322

The P-value is less than the significance level of 0.05, so it is statistically significant.

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-tests determine if a linear relationship exists with a minimum of one predictor

value. After checking if a linear relationship exists, a T-test will be conducted to

determine if 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.

0.819

The value for R squared (0.819) means that 81.9% of this data fits the regression

model. This means that about 81.9% of total variation in MPG is account for by the

linear regression model including HP as horsepower and WT as weight as

predictors.

Unformatted Attachment Preview

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. H0: β1 = β2 = 0 Ha: at least one βn ≠ 0 for n = 1, 2. Ho: The regression model is not significant. H1: The regression model is significant b. Report the level of significance. level of significance α = 0.05 c. Include the test statistic and the P-value. (Hint: F-St ...
Purchase document to see full attachment