sample - Using Minitab for Regression Analysis: An extended...

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Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to generate the statistical measures discussed in Anderson Sweeney and Williams . The data here have already been input, and stored in C1 and C2. The scatter plot below is similar to A, S, & W Figure 14.3 on page 559. You can find additional discussion of scatter plots in the Minitab Handbook on pages 158-63. This is formed using GRAPH > SCATTERPLOT > SIMPLE Fertilizer Crop Yield 700 600 500 400 300 200 100 80 70 60 50 40 Scatter Plot of Yield against Fertilizer There seems to be a strong positive relationship between these two variables. One way to measure the strength of the relationship is with the correlation coefficient. For discussion see A, S & W, pages 110-12, 572-3 or the Minitab Handbook , pages 296-97. In Minitab 14 you can compute a correlation by clicking on STAT > BASIC STATISTICS > CORRELATION. Minitab uses formula (3.12) on page 110 of A, S & W to do the calculation. MTB > Correlation 'Fertilizer' 'Crop Yield'. Correlations: Fertilizer, Crop Yield Pearson correlation of Fertilizer and Crop Yield = 0.920 P-Value = 0.003
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We can overlay a fitted line on our scatter plot. We can obtain the plot either with or without the estimated regression equation. To produce a plot with the estimated equation, use STAT > REGRESSION > FITTED LINE PLOT, and selecting the Linear alternative (See Minitab Handbook, pp. 320-21). Fertilizer Crop Yield 700 600 500 400 300 200 100 80 70 60 50 40 S 5.96118 R-Sq 84.5% R-Sq(adj) 81.5% Fitted Line Plot Crop Yield = 36.43 + 0.05893 Fertilizer Or this simpler picture from GRAPH > SCATTERPLOT > WITH REGRESSION Fertilizer 700 600 500 400 300 200 100 80 70 60 50 40 Scatterplot of Crop Yield vs Fertilizer
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To estimate a regression line, the command in Minitab is “Regress,” which we access by clicking on STAT > REGRESSION > REGRESSION. We fill it in as shown, with the Y variable entered into “Response:” and the X variable entered into “Predictors:” To predict, we click on the box labeled Options… and insert the X value (the value of Fertilizer) for which we would like to predict. Here, I chose to predict for X=550.
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By clicking on the box labeled Storage…, I can ask Minitab to store some information for me to use later: the residuals, the standardized residuals, the leverages, and the fitted values. If you are uncertain about what these terms mean, you can consult ASW.
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sample - Using Minitab for Regression Analysis: An extended...

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