Scenario: Crammer Nation University wants to develop a regression equation to predict the "Number of Recruits" a given fraternity will receive this rush season given the "Parties" that fraternity threw last year and the average "GPA" of the fraternity. They took a sample of 52 fraternities on campus, resulting in the regression output below.
Is there a meaningful, linear relationship in this model? Provide support for your claim using a hypothesis test with an alpha level of 0.05.
Clue | Insight |
---|---|
We're supporting our claim with a "hypothesis test". | We're working with hypothesis tests. |
The claim is whether or not "meaningful, linear relationship in this model". | We're working with the entire model. |
Given that we're assessing the significance of the model... | We'll use the F Ratio. |
Assumption | Validate |
---|---|
Linearity | For the sake of this example, let's assume the underlying scatterplot for each predictor variable shows a linear relationship. ✅ |
Independence | We can assume that each chapter's parties thrown, GPA, and recruits received don't impact one another. ✅ (Ex: Delta Apple Pi's parties, GPA, and recruits don't impact Alpha Blueberry Pi's.) |
Equal Variance | For the sake of this example, let's assume the residual plot for each predictor variable shows equal variance. ✅ |
Normality | For the sake of this example, let's assume the residuals for each predictor variable are normally distributed. ✅ |
H_{0}: β_{Parties} = β_{GPA} = 0
H_{a}: At least one β ≠ 0
It's in the regression output!
F Ratio = 167.67
It's in the regression output!
p-value < 0.0001
α = 0.05
Considering our p-value is less than 0.0001 which is less than our alpha level of 0.05, this means we'll reject the null hypothesis!
Answer: Since our p-value is < 0.0001 is less than our alpha level of 0.05, we reject the null hypothesis and do have enough evidence to support the alternative hypothesis, which states that the model is significant in predicting the "Number of Recruits" for a given fraternity at Crammer Nation University.
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Your university wants to predict the “Sign-Ups” at a student organization receives at mega fair based on the social media “Posts” made by that organization throughout the semester. They randomly sample 30 student organizations, resulting in the following regression analysis.
Is there a meaningful, linear relationship in this model? Provide support for your claim using a hypothesis test with an alpha level of 0.05.
Since our p-value of is (less / greater) than than our alpha level of , we (reject / fail to reject) the null hypothesis and (do / do not) have enough evidence to support the alternative hypothesis.
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