Computer Lab Session #4: Linear Regression Analysis with MINITAB | Lab Reports Statistics

Computer Lab Session #4

Load again the file MASSCOLL.MTW from the Minitab example data sets, Student 12

subdirectory, and consider the two simple linear regressions of y=“%WhoGrad” (percentage

of students graduating) on x1=“CSAT” (median combined SAT math and verbal score), and

onx2=“SFRatio” (student faculty ratio)

Does the data contain evidence that, on average, for each additional point in CSAT the

percentage of students graduating increases by less than 0.1 points? (you have to set up and

perform a test of hypothesis to answer this question, and it will require using the t

distribution – this is not a test for which you can find the p-value in the regression output).

For both regressions, produce again the fitted line plot with 95% confidence interval for the

mean response and 95% prediction interval “bands” superimposed. Now that you know the

technical details underlying these intervals, comment and interpret.

In addition, compute 95% confidence intervals for percentage of students graduating and

95% prediction intervals for percentage of students graduating in correspondence of the 10,

25, 50, 75 and 90 percentiles of CSAT, and of SFratio. Comment and interpret. Use

Stat > Regression > Regression, in “Options”, “Prediction Intervals for New

Observations”.

For both regressions, you will find an ANOVA table in the default output of Stat >

Regression > Regression. Make sure you can interpret the various terms in these tables in

relation to the material introduced in the lectures. Check that the F values in the Analysis of

variance Tables coincide with the squares of the T values for the two slopes. Relate the

values in the decomposition SSTot = SSR + SSE to the value of the determination

coefficient R2 = SSR/SSTot in each regression.

As a pointer for the next lectures, for each regression, produce:

• The plot of (regular) residuals versus the predictor variable. Use Stat > Regression >

Regression, in “Graphs”. In conjunction with the “Unusual observations” part of the

regression output, this should give you an idea of whether there are unusual observations

in the data. Try to understand intuitively what is meant by “unusual” here.

• The histogram of the (regular) residuals. Use again Use Stat > Regression >

Regression, in “Graphs”. Intuitively, is this histogram telling you something useful

concerning the assumption of normal errors for the underlying simple regression model?

Why so?

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Computer Lab Session #

Load again the file MASSCOLL.MTW from the Minitab example data sets, Student 12 subdirectory, and consider the two simple linear regressions of y=“%WhoGrad” (percentage of students graduating) on x 1 =“CSAT” (median combined SAT math and verbal score), and onx 2 =“SFRatio” (student faculty ratio)

Does the data contain evidence that, on average, for each additional point in CSAT the percentage of students graduating increases by less than 0.1 points? (you have to set up and perform a test of hypothesis to answer this question, and it will require using the t distribution – this is not a test for which you can find the p-value in the regression output).

For both regressions, produce again the fitted line plot with 95% confidence interval for the mean response and 95% prediction interval “bands” superimposed. Now that you know the technical details underlying these intervals, comment and interpret.

In addition, compute 95% confidence intervals for percentage of students graduating and 95% prediction intervals for percentage of students graduating in correspondence of the 10, 25, 50, 75 and 90 percentiles of CSAT, and of SFratio. Comment and interpret. Use Stat > Regression > Regression , in “Options” , “Prediction Intervals for New Observations”.

For both regressions, you will find an ANOVA table in the default output of Stat > Regression > Regression. Make sure you can interpret the various terms in these tables in relation to the material introduced in the lectures. Check that the F values in the Analysis of variance Tables coincide with the squares of the T values for the two slopes. Relate the values in the decomposition SSTot = SSR + SSE to the value of the determination coefficient R 2 = SSR/SSTot in each regression.

As a pointer for the next lectures, for each regression, produce:

The plot of (regular) residuals versus the predictor variable. Use Stat > Regression > Regression , in “Graphs”. In conjunction with the “Unusual observations” part of the regression output, this should give you an idea of whether there are unusual observations in the data. Try to understand intuitively what is meant by “unusual” here.
The histogram of the (regular) residuals. Use again Use Stat > Regression > Regression , in “Graphs”. Intuitively, is this histogram telling you something useful concerning the assumption of normal errors for the underlying simple regression model? Why so?

Computer Lab Session #4: Linear Regression Analysis with MINITAB, Lab Reports of Statistics

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