Please review my results and peers' results and provide some analysis and interpretation:

1. Interpret your peer's coefficient of determination. How does it compare with yours?
2. How do the results of your peers' t-tests compare with yours?
3. Would you recommend this regression model to the car rental company? Why or why not?

My results

Define the null and alternative hypothesis in mathematical terms and in words.

Report the level of significance.

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

Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?

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Ho : All the beta coefficient are equal to zero.

H1 : At least one of the beta coefficient is not equal to zero.

An F-test is conduct to check this hypothesis and summary of the test is given

Fstatistic = 64.53

pvalue = 5.18e-11

We check the pvalue from the ANOVA table (indicated as Significance F)

If the pvalue is less than 0.05(level of significance- alpha) , we reject the null hypothesis and conclude that the regression equation as whole is valid and statistical significant.

If the pvalue is greater than 0.05(level of significance- alpha) , we fail reject the null hypothesis and conclude that the regression equation as whole is not valid or significant.

We find that the pvalue = 0, which is less than 0.05, hence we reject the null hypothesis and conclude that the regression equation is significant.

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, p> |t|, for weight in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.

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Slope coefficient for the weight variable = -3.9360

Hypothesis test:

For each variable, we take beta coefficient do test the following hypothesis.

We check the pvalue associated with that variable,

if the pvalue is less than 0.05(level of significance specified), then we reject the null hypothesis and conclude that the variable is significant or is statistically different from zero. Hence it is significant predictor of y.

if the pvalue is greater than 0.05(level of significance specified), then we fail to reject the null hypothesis and conclude that the variable is not significant or is not statistically different from zero. Hence it is not significant predictor of y and can be dropped from the regression.

In this case the tstat = -5.927 and the pvalue = 0.000, hence since the pvalue is less than 0.05, we reject the null hypothesis and conclude that weight is significant predictor of y.

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, p> |t|, for horsepower in Python output. Recall that this is the individual t-test for the beta parameter.) See Step 5 in the Python script.

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Slope coefficient for the horsepower variable = -0.0310

Hypothesis test:

For each variable, we take beta coefficient do test the following hypothesis.

We check the pvalue associated with that variable,

if the pvalue is less than 0.05(level of significance specified), then we reject the null hypothesis and conclude that the variable is significant or is statistically different from zero. Hence it is significant predictor of y.

if the pvalue is greater than 0.05(level of significance specified), then we fail to reject the null hypothesis and conclude that the variable is not significant or is not statistically different from zero. Hence it is not significant predictor of y and can be dropped from the regression.

In this case the tstat = -3.276 and the pvalue = 0.003, hence since the pvalue is less than 0.05, we reject the null hypothesis and conclude that horsepower is significant predictor of y.

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?

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In the Ftest we check if the regression model is significant is as whole. Even if the model has one significant variable, the model will be reported as significant.

The individual ttest helps use to check if a particular variable is significant predictor of y or not. If not it can be dropped from the regression equation.

What is the coefficient of determination of your multiple regression model from Module Six? Provide appropriate interpretation of this statistic.

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Coefficient of determination(rsqaure) = 0.827

It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 82.7% hence the model is good

Peer results

Hello everyone,

1.

A. The null hypothesis is that the regression model isn't significant. The alternative hypothesis is that the regression model is significant.

B. The level of significance is 0.05.

C. F-Statistic=66.86

P-value = 0.0000

D. Since the p-value (0.0000) is less than the level of significance (0.05) we have to reject the null hypothesis so thats means we have to accept the alternative hypothesis. This means that the regression model is significant.

2.

The slope coefficient for weight is -3.9376.

The coefficient is rejected because the p-value is less than 0.05. This means that the coefficient is significant.

3.

The slope coefficient for horsepower is -0.0317.

The coefficient is rejected because the p-value is less than 0.05. This means that the coefficient is significant.

4. The overall f-test helps you get an idea if overall they are significant but the individual t-tests let you know more specifically which are or aren't significant.

5. The coefficient of determination is 0.832. The coefficient of determination is interpreted as 83.2% and that means that its close to matching the expectation of the equation. It compares to factors to each other and the more similar they are the closer to 100% the coefficient of determination is.

Best regards,

Brian