Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 11 Simple Linear Regression.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Chapter 11

Simple Linear Regression


11.1

Probabilistic Models

11 - 3 Copyright © 2013 Pearson Education, Inc.. All rights reserved.

Figure 11.1 Possible reaction times y for five different drug percentages x


Procedure


Figure 11.2 The straight-line model


Procedure


11.2

Fitting the Model: The Least Squares Approach


Table 11.1


Figure 11.3 Scatterplot for data in Table 11.1


Figure 11.4 Visual straight line fitted to the data in Figure 11.3


Table 11.2


Definition


Formula


Table 11.3


Figure 11.5 The line fitted to the data

ˆ .1 .7y x


Table 11.4


Figure 11.6a SAS printout for the time-drug regression


Figure 11.6b SPSS printout for the time-drug regression


Figure 11.6c MINITAB printout for the time-drug regression


Procedure


Table SIA11.1


Figure SIA11.1 MINITAB scatterplot of dowsing data


Figure SIA11.2 MINITAB simple linear regression for dowsing data


11.3

Model Assumptions


Figure 11.7 The probability distribution of


Procedure


Figure 11.8 SAS printout for the time-drug regression


Procedure


11.4

Assessing the Utility of the Model: Making Inferences about the Slope 1


Figure 11.9 Graph of the straight-line model when the slope is zero, i.e., 0y


Procedure


Figure 11.10 Sampling distribution of 1̂


Procedure


Definition


Figure 11.11 Rejection region and calculated t value for testing versus

1: 0H 0 1: 0H


Figure 11.12 MINITAB printout for the time-drug regression


Procedure


Definition


Figure 11.13 SPSS printout with 95% confidence intervals for the time-drug regression betas


Figure SIA11.3 MINITAB simple linear regression for dowsing data


11.5

The Coefficients of Correlation and Determination


Procedure


Figure 11.14 Values of r and their implications


Table 11.5


Figure 11.15 MINITAB correlation printout and scatterplot for Example 11.4


Procedure


Definition


Figure 11.16 A comparison of the sum of squares of deviations for two models


Procedure


Table 11.6


Figure 11.17 Portion of SPSS printout for time-drug regression


Procedure


Figure SIA11.4 MINITAB printouts with coefficients of correlation and determination for the dowsing data


Using the Model for Estimation and Prediction

11.6


Figure 11.18 Estimated mean value and predicted individual value of reaction time y for x = 4


Procedure


Figure 11.19 MINITAB printout giving 95% confidence interval for E(y) and 95% prediction interval for y


Figure 11.20 Error in estimating the mean value of y for a given value of x


Figure 11.21 Error in predicting a future value of y for a given value of x


Figure 11.22 Confidence intervals for mean values and prediction intervals for new values


Figure SIA11.5 MINITAB prediction interval for dowsing data


A Complete Example

11.7


Table 11.7


Figure 11.23 SAS printout for fire damage regression


Figure 11.24 MINITAB scatterplot with least squares line for fire damage regression analysis

Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 11 Simple Linear Regression.

Documents

Transcript of Copyright © 2013 Pearson Education, Inc. All rights reserved Chapter 11 Simple Linear Regression.