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(|T_{90}|>2.185)=2*P(T_{90}<-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:

College Graduation Rates. Data from the College
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t-ratio
P-value
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Constant
-13.9288
30.51
-0.457
0.6497
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Budget ($M)
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s = 57.94
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