1.True/False problems

(a)The larger the coefficient of determination R², the better the model fits the data.

(b)The prediction interval for y is the narrowest when the given x value is at the mean.

2.Suppose simple linear regression is applied to analyze a data set with sample size n=15, the estimated slope Beta1=-2.5 and the determination of coefficient R²=.81.Based on this information, answer the following questions.

(a)Find the coefficient of correlation r.

(b)Find the ANOVA F test statistics, and answer if the simple linear regression model is useful to analyze this data set. (note: you can find the F critical value via R function qf(.95,1,13) )