Lesson 14 - R Chapter 14 Review

Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review exercises Use the technology to compute statistical data in the chapter

Problem 1 To perform inference in a least-squares model, the distribution of the response variable y, for a specific explanatory variable x, must 1)Have a standard deviation of 1 2)Have a normal distribution 3)Have a mean equal to its standard deviation 4)Have all of the above

Problem 2 A hypothesis test for the slope, in a least- squares regression model, can be performed using 1)The mean, compared to the median distribution 2)A sum of squares, compared to a chi-square distribution 3)A t-score, compared to the t-distribution 4)The ratio with the intercept, compared to the F distribution

Problem 3 A researcher has found an appropriate least- squares regression model. To predict the mean value of the response variable y, for a specific explanatory variable x, she should 1)Perform a hypothesis test on the intercept 2)Calculate a prediction interval for an individual response 3)Perform a hypothesis test on the slope 4)Calculate a confidence interval for the mean response

Problem 4 For a least-squares regression model, as a researcher collects more and more points (larger values of n), the confidence interval for a mean response 1)Should, in general, become narrower 2)Should, in general, become more normal 3)Should, in general, become more symmetric 4)Should, in general, become closer to the prediction interval for an individual response

Problem 5 A multiple regression model differs from a simple linear regression model in that the multiple regression model 1)Does not require linear relationships 2)Can not be analyzed using inferential techniques 3)Involves more than one explanatory variable 4)Involves more than one response variable

Problem 6 In developing the “best” multiple regression model 1)None of the explanatory variables should ever be dropped to reach the final model 2)If a specific explanatory variable has a large correlation with the response variable, it should be included in the final model 3)Each explanatory variable in the final model should have a coefficient that is significantly different from 0 4)Only explanatory variables with positive correlations should be included

Things to Remember In the Least Square Regression model: –R² gives us the % of the variation in the response variable explained by the model –the mean of the response variable depends on the linearity of the explanatory variable –the residuals must be normally distributed with constant error variance –the ε i will be normally distributed (0,σ²) –we are estimating two values (b 0 b 1 ) and therefore lose 2 degrees of freedom in the t-statistic –the prediction interval for an individual response will be wider than the confidence interval for a mean response –procedures are robust

Things to Remember In Multiple Regression models: –the adjusted R² gives us the % of the variation in the response variable explained by the model R² is adjusted based on # of sample and number of explanatory variables in the model –multicollinearity may be a problem if a high linear correlation exists between explanatory variables Rule: |correlation| > 0.7 then multicollinearity possible –the procedure used in our book for multiple regression modeling is called backwards step-wise regression Rule: remove explanatory variable with highest p-value and then rerun the model check adjusted R² values

Summary and Homework Summary –In a least squares regression model, we can test if the slope and the intercept differ significantly from 0 –We can compute confidence and prediction intervals to describe predicted values of the response variable y –We can include multiple explanatory variables x to form a multiple regression model Homework –pg 784 – 787; 3, 5, 7