Practice Lab for Test 1 - Applied Regression Analysis | STAT 462, Assignments of Statistics

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Practice Lab for Test

Consider again the simple linear regression of y=%WhoGrad on x=CSAT in the

MASSCOLL.MTW data set. Reproduce and be sure you are familiar with the following output.

Descriptive Statistics: %WhoGrad, CSAT

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q %WhoGrad 52 4 72.38 2.39 17.26 38.00 58.25 73.00 85. CSAT 53 3 1001.4 23.1 168.5 764.0 877.5 951.0 1135.

Variable Maximum %WhoGrad 100. CSAT 1400.

Correlations: %WhoGrad, CSAT

Pearson correlation of %WhoGrad and CSAT = 0.

Regression Analysis: %WhoGrad versus CSAT

The regression equation is %WhoGrad = 2.4 + 0.0700 CSAT 49 cases used, 7 cases contain missing values

Predictor Coef SE Coef T P Constant 2.39 10.62 0.22 0. CSAT 0.07005 0.01032 6.79 0.

S = 11.9236 R-Sq = 49.5% R-Sq(adj) = 48.4%

Analysis of Variance Source DF SS MS F P Regression 1 6548.1 6548.1 46.06 0. Residual Error 47 6682.1 142. Total 48 13230.

700 800 900 1000 1100 1200 1300 1400

100 90 80 70 60 50 40 CSAT

%WhoGrad

SR-Sq 11.923649.5% R-Sq(adj) 48.4%

Fitted Line Plot %WhoGrad = 2.39 + 0.07005 CSAT

700 800 900 1000 1100 1200 1300 1400

30 20 10 0

• CSAT

Residual

Residuals Versus CSAT (response is %WhoGrad)

Make sure you can answer the following questions:

What are the least square estimates for the intercept and slope of the regression line?

Assuming normality of errors, what are the 95% confidence intervals for slope and

intercept?

Assuming normality of the errors, how do you test whether the slope in the regression is

significantly different from zero?

What is the share of the overall variability in the response that is explained by the regression?

What do the quantities in the ANOVA table represent?

Consider the plot of residuals versus predictor:

Is there visual evidence that the relationship between mean response and predictor is non-linear?

Is there visual evidence that the error variance is not constant?

Is there visual evidence of outliers?

Construct a point estimate for the mean response, a 95% Confidence Interval for the mean

response, and a 95% prediction interval for the response, when the CSAT score is 1200.

Make sure you are able to answer these questions based on information in the main Minitab

output, as presented above.