Question

(1 point) College Graduation Rates.  Data from the College Results Online website compared the 2011 graduation rate and school size for 92 similar-sized public universities and colleges in the United States. Statistical software was used to create the linear regression model using size as the explanatory variable and graduation rate as the response variable. Summary output from the software and the scatter plot are shown below. Round all calculated results to four decimal places.

Coefficients	Estimate	Std. Error	t value	Pr(>|t|)
Intercept	41.442572	4.427554	9.36	6.1e-15
Size	0.001051	0.000481	2.18	0.031

Residual standard error: 13.1 on 90 degrees of freedom
Multiple R-squared: 0.0504,Adjusted R-squared: 0.0398  
F-statistic: 4.77 on 1 and 90 DF, p-value: 0.031

1. Write the equation for the regression line for predicting graduation rate from the size of the school.

Grad Rate =  +  (Size)

2.Complete the following sentence:

% of the variation in  ? Graduation rate Size School  can be explained by the linear relationship to  ? Graduation rate Size School .

Do the data provide strong evidence (?α = 0.05) that the size of the school is associated with the graduation rate? Conduct a t-test using the information given in the R output and the hypotheses

?0:?1=0H0:β1=0 vs. ??:?1≠0HA:β1≠0

Use ?α = 0.05.

3. Test statistic =

4. Degrees of freedom =

5. P-value =

6. Based on the results of this hypothesis test, there  ? is is not  a significant linear relationship between the explanatory and response variables.

7. Calculate a 95% confidence interval for the slope, ?1β1. (  ,   )

Answer 1

1. Grad Rate =  41.442572+  0.001051(Size)

2. 3.98% of the variation in Graduation rate School can be explained by the linear relationship Size School.

3. The test statistic is given by:

4. Degrees of freedom = 92-2 = 90

5. P-value = P(|T₉₀|>2.185)=2*P(T₉₀<-2.185) = 0.0315

6. Based on the results of this hypothesis test, there is a significant linear relationship between the explanatory and response variables.

7. 95% confidence interval for the slope, ?1 is given by: