# Minitab Help 7: Transformations & Interactions

### Word recall (log-transforming a predictor)

- Perform a linear regression analysis of prop on time.
- Create a fitted line plot.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Conduct regression error normality tests and select Anderson-Darling.
- To create a log(time) variable, select Calc > Calculator, specify the name of the new variable (lntime, for example) in the box labeled "Store result in variable," and type "log(time)" in the box labeled "Expression." Select OK and the new variable should appear in your worksheet.
- Perform a linear regression analysis of prop on log(time).
- Repeat diagnostic plots and normality test.
- Use Calc > Calculator to create prop^-1.25 variable and Perform a linear regression analysis of prop^-1.25 on time.
- Repeat diagnostic plots and normality test.
- Use prop on log(time) model to find:
- 95% prediction interval for prop at time 1000. Use Find a confidence interval and a prediction interval for the response and specify 6.91 for the individual value of log(time).
- 95% confidence interval for expected change in prop for a 10-fold increase in time. To display confidence intervals for the model parameters (regression coefficients) click "Results" in the Regression Dialog and select "Expanded tables" for "Display of results."

### Mammal gestation (log-transforming the response)

- Perform a linear regression analysis of Gestation on Birthwgt.
- Create a fitted line plot.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Conduct regression error normality tests and select Anderson-Darling.
- Use Calc > Calculator to create log(Gestation) variable and Perform a linear regression analysis of log(Gestation) on Birthwgt.
- Repeat diagnostic plots and normality test.
- Use log(Gestation) on Birthwgt model to find:
- 95% prediction interval for Gestation for a Birthwgt of 50. Use Find a confidence interval and a prediction interval for the response.
- 95% confidence interval for proportional change in median Gestation for a 1 pound increase in Birthwgt. To display confidence intervals for the model parameters (regression coefficients) click "Results" in the Regression Dialog and select "Expanded tables" for "Display of results."
- 95% confidence interval for proportional change in median Gestation for a 10 pound increase in Birthwgt.

### Shortleaf pine trees (log-transforming both response and predictor)

- Perform a linear regression analysis of Vol on Diam.
- Create a fitted line plot.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Conduct regression error normality tests and select Anderson-Darling.
- Use Calc > Calculator to create log(Diam) variable and Perform a linear regression analysis of Vol on log(Diam).
- Repeat diagnostic plots and normality test.
- Use Calc > Calculator to create log(Vol) variable and Perform a linear regression analysis of log(Vol) on log(Diam).
- Repeat diagnostic plots and normality test.
- Use log(Vol) on log(Diam) model to find:
- 95% confidence interval for median Vol for a Diam of 10. Use Find a confidence interval and a prediction interval for the response and specify 2.303 for the individual value of log(Diam).
- 95% confidence interval for proportional change in median Vol for a 2-fold increase in Diam. To display confidence intervals for the model parameters (regression coefficients) click "Results" in the Regression Dialog and select "Expanded tables" for "Display of results."

### Underground air quality (interactions)

- Select Graph > 3D Scatterplot (Simple) to create a 3D scatterplot of the data.
- Create interaction variables and Perform a linear regression analysis of Vent on O2 + CO2 + Type + TypeO2 + TypeCO2 + CO2O2.
- Alternatively, Perform a linear regression analysis of Vent on O2 + CO2 + Type, but before clicking "OK," click "Model," select O2, CO2, and Type in the "Predictors" box, change "Interactions through order" to "2" and click "Add." You should see "Type*O2," "Type*CO2," and "CO2*O2" appear in the box labeled "Terms in the model."
- Click "Options" in the regression dialog to select Sequential (Type I) sums of squares for the Anova table.
- Calculate partial F-statistic by hand and Find an F-based P-value.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Perform a linear regression analysis of Vent on O2 + CO2 + Type.
- Create residual plots and select "Residuals versus fits" (with regular residuals).
- Conduct regression error normality tests and select Anderson-Darling.

### Bluegill fish (polynomial regression)

- Create a basic scatterplot.
- Use Calc > Calculator to create age-squared variable and Perform a linear regression analysis of length on age + agesq.
- Alternatively, Perform a linear regression analysis of length on age, but before clicking "OK," click "Model," change "Terms through order" to "2" and click "Add." You should see "age*age" appear in the box labeled "Terms in the model."
- Create a fitted line plot and select "Quadratic" for the "Type of regression model."
- Find a confidence interval and a prediction interval for the response.

### Experiment yield (polynomial regression)

- Perform a linear regression analysis of Yield on Temp.
- Create a fitted line plot.
- Use Calc > Calculator to create Temp-squared variable and Perform a linear regression analysis of Yield on Temp + Tempsq.
- Alternatively, Perform a linear regression analysis of Yield on Temp, but before clicking "OK," click "Model," change "Terms through order" to "2" and click "Add." You should see "Temp* Temp" appear in the box labeled "Terms in the model."
- Create a fitted line plot and select "Quadratic" for the "Type of regression model."

### Chemical odor (polynomial regression)

- Use Calc > Calculator to create squared variables and Perform a linear regression analysis of Odor on Temp + Ratio + Height + Tempsq + Ratiosq + Heightsq.
- Alternatively, Perform a linear regression analysis of Odor on Temp + Ratio + Height, but before clicking "OK," click "Model," select Temp, Ratio, and Height in the "Predictors" box, change "Terms through order" to "2" and click "Add." You should see "Temp* Temp," "Ratio*Ratio," and "Height*Height" appear in the box labeled "Terms in the model."
- Perform a linear regression analysis of Odor on Temp + Ratio + Height + Tempsq + Ratiosq (remove the "Height*Height" term by clicking "Model," selecting "Height*Height" in the box labeled "Terms in the model," and clicking "X").