5. Regression in the Toolbar of Minitab’s Help

7/27/2019 5. Regression in the Toolbar of Minitabs Help

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Regression in the Toolbar of Minitabs Help

1.Example ofsimple linear regression

You are a manufacturer who wants to obtain a quality measure on a

product, but the procedure to obtain the measure is expensive. There is

an indirect approach, which uses a different product score (Score 1) in

place of the actual quality measure (Score 2). This approach is less costly

but also is less precise. You can use regression to see if Score 1 explains a

significant amount of variance in Score 2 to determine if Score 1 is an

acceptable substitute for Score 2.

1 Open the worksheet EXH_REGR.MTW.

2 Choose Stat > Regression > Regression.

3 In Response, enter Score2.

4 In Predictors, enter Score1.

5 Click OK.

Session window output


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Interpreting the results

Minitab displays the results in the Session window by default.

The p-value(5) in the Analysis of Variance table(13) (0.000), indicates

that the relationship between Score 1 and Score 2 is statistically

significant(10) at an -level(2) of 0.05. This is also shown by the p-value

for the estimated coefficient(14) of Score 1, which is 0.000.

The R2(15) value shows that Score 1 explains 95.7% of the variance in

Score 2, indicating that the model fits the data extremely well.

Observation 9 is identified as an unusual observation(16) because its

standardized residual

(17)

is less than -2. This could indicate that thisobservation is an outlier. See Identifying outliers.

Because the model is significant and explains a large part of the variance

in Score 2, the manufacturer decides to use Score 1 in place of Score 2 as

a quality measure for the product.

2. Example of multiple regressions

As part of a test of solar thermal energy, you measure the total heat

flux from homes. You wish to examine whether total heat flux (HeatFlux)
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can be predicted by the position of the focal points in the east, south, and

north directions. Data are from [27]. You found, using best subsets

regression, that the best two-predictor(18) model included the variables

North and South and the best three-predictor added the variable East. Youevaluate the three-predictor model using multiple regression.


2 Choose Stat > Regression > Regression.

3 In Response, enter HeatFlux.

4 In Predictors, enter East South North.

5 Click Graphs.

6 UnderResiduals for Plots, chooseStandardized.

7 Under Residual Plots, choose Individual Plots. Check

Histogram of residuals, Normal plot of residuals, and

Residuals versus fits. Click OK.

8 Click Options. Under Display, check PRESS and predicted R-

square. Click OKin each dialog box.

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Session window output The p-value(5) in the Analysis of Variance table(13) (0.000) shows that

the model estimated by the regression procedure is significant(10) at an

-level(2) of 0.05. This indicates that at least one coefficient is different

from zero.

The p-values for the estimated coefficients(14) of North and South are

both 0.000, indicating that they are significantly related to HeatFlux.

The p-value for East is 0.092, indicating that it is not related to

HeatFlux at an -level(2) of 0.05. Additionally, the sequential sum of

squares(19) indicates that the predictor East doesn't explain a

substantial amount of unique variance. This suggests that a model with

only North and South may be more appropriate.

The R2(15) value indicates that the predictors explain 87.4% of the

variance in HeatFlux. The adjusted R2(20) is 85.9%, which accounts for

the number of predictors in the model. Both values indicate that the

model fits the data well.

The predicted R2(21) value is 78.96%. Because the predicted R2 value is

close to the R2 and adjusted R2 values, the model does not appear to

be overfit and has adequate predictive ability.

Observations 4 and 22 are identified as unusual because the absolute

value of the standardized residuals are greater than 2. This may
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indicate they are outliers(22). See Checking your model, Identifying

outliers, and Choosing a residual type.

Graph window output

The histogram

(23)

indicates that outliers may exist in the data, shownby the two bars on the far right side of the plot.

The normal probability plot(24) shows an approximately linear pattern

consistent with a normal distribution(25). The two points in the upper-

right corner of the plot may be outliers(22). Brushing the graph identifies

these points as 4 and 22, the same points that are labeled unusual

observations in the output. See Checking your model and Identifying

outliers. The plot of residuals(11) versus the fitted values(26) shows that the

residuals(11) get smaller (closer to the reference line) as the fitted

values increase, which may indicate the residuals have non-constant

variance. See [9] for information on non-constant variance.

3. Example of Fitted Regression Line

You are studying the relationship between a particular machinesetting and the amount of energy consumed. This relationship is known to

have considerable curvature, and you believe that a log transformation of

the response variable(18) will produce a more symmetric error(32)

distribution. You choose to model the relationship between the machine

setting and the amount of energy consumed with a quadratic model(33).


2 Choose Stat > Regression > Fitted Line Plot.3 In Response (Y), enter EnergyConsumption.

4 In Predictor (X), enter MachineSetting.

5 Under Type of Regression Model, choose Quadratic.

6 Click Options. Under Transformations, check Logten of Yand

Display logscale for Y variable. Under Display Options, check

Display confidence interval and Display prediction interval.

Click OKin each dialog box.

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The quadratic model (p-value(9) = 0.000, or actually p-value

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5. Regression in the Toolbar of Minitab’s Help