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Inference for Regression

Formulas:• Hypothesis test:

bSE

bt

statistic of SD

parameter - statisticstatisticTest

Median SAT

Expenditure

Grad Rate

1065 7970 49950 6401 331045 6285 37990 6792 49950 4541 22970 7186 38980 7736 391080 6382 521035 7323 531010 6531 411010 6216 38930 7375 371005 7874 451090 6355 571085 6261 48

The data on six-year graduation rate (%), student-related expenditure per full-time student, and median SAT score for a random sample of the primarily undergraduate public universities in the US with enrollments between 10,000 and 20,000 were taken from College Results Online, The Education Trust.

We would like to know if there is

.

For a test of a linear relationship, the null hypothesis is usually expressed as:

In this context, this means

Conjecture:

We suspect that increased expenditures can be used to predict graduation rates.

H0: b = 0 Where b is the true slope between expenditures and graduation rates.

Ha: b > 0

Assumptions :• Have an SRS of colleges• Since the residual plot is randomly scattered, Expenditures and Grad rates are linear

• Since the points are evenly spaced across the LSRL on the scatterplot, sy is approximately equal for all values of grad rate

• Since the boxplot of residual is approximately symmetrical, the responses are approximately normally distributed.

Test statistic: Linear Regression t-test

05.13

046.

81.100254.

00046.

df

valuep

SE

bt

b

t

bSEb

Since the p-value < a, I reject H0. There is sufficient evidence to suggest that expenditures can be used to predict graduation rate.

Now for some computer output

Give the equation of the line, in the context of the problem.  

What does the R-Sq value tell us?

 Hypothesis Test:

 Conjecture / Hypotheses

 Conditions

 Mechanics

Conclusion