ST FINAL

A correlation coefficient value of rXY = 0 indicates that there is no relationship of any sort, other than random, between X and Y.

False

A correlation coefficient value of rXY = 0.97 indicates a strong linear association, while a correlation coefficient value of

rXY = −0.97 indicates a weak linear association.

False

For a set of X-Y data, if the large values of X are associated with the small values of Y (and visa versa), then the correlation coefficient will be negative.

True

In simple linear regression, a single explanatory variable is used help explain the variability in a designated response variable.

True

In simple linear regression, our criterion for the best fitting line is the line that minimizes the sum of the squared errors.

True

In simple linear regression, one of the assumptions is that the variability of the errors is constant for all levels of X.

False

In correlation analysis or regression analysis, the steeper the line, the stronger the correlation of the two variables.

False

In regression, “extrapolation” refers to the practice of making predictions outside the range of the sample data.

True

In simple linear regression, the sum of the residuals (errors) is always zero.

True

For the same set of X-Y data, the correlation coefficient and the slope of the regression line always have the same sign.

True

In simple linear regression, the sum of the residuals (errors) is always zero.

True

In general, the more variable the data points are about the regression line, the larger the value of R2.

False

In simple regression, if SSE is relatively small, R2 will tend to be large.

True

The Total Sum-of-Squares measures the variability in the response variable and does not depend on any predictor variable

True

In a simple regression analysis, suppose that SST = 150 and SSE = 30. The

value of R2 is then _________.

80%

In a simple regression analysis, the correlation coefficient is rXY = –0.70. The proportion of the variability in Y that is explained by X is _________.

49%

In a properly fit regression model, the Residuals vs. Fitted Values plot should exhibit a linear pattern.

False

A high leverage point may cause a significant increase in R2, even if it does not fit the pattern of the rest of the data.

True

In simple regression, an R2 value of 0.80 indicates that 80% of the variability in the response variable (Y) is explained by the predictor variable (X).

True

In a simple regression analysis a value of 0.955 for the F-statistic in the ANOVA Table indicates that the X- variable is not useful in predicting the response (Y-variable).

True

In simple regression, a t-value of 7.8 for the slope coefficient indicates that X is a useful predictor of Y.

True

In a multiple regression analysis, the variable with the largest estimated coefficient is typically the most useful predictor.

False

In a multiple regression analysis, predictor variables that are, by themselves, useful in predicting the response, may not be useful in the presence of other predictor variables.

True

In a multiple regression analysis, if MSE = 100 and MSR = 85, we would conclude that the predictor variables are not useful for predicting the response variable.

True

In a multiple regression analysis, a high degree of correlation between and among the predictor variables makes for a better model.

False

In a multiple regression analysis, the full model, using all available predictors, will have the largest value of R2.

True

In a simple regression of Y and X, if the sample correlation between Y and X is –1, then SSE must be equal to zero.

True

MSR is an unbiased estimate of the error variance, σ2.

False

In simple linear regression, one of the assumptions of the model is that the response variable is independent of the explanatory variable.

False

In simple regression, if the estimate b1 is large in absolute value, then the model will produce a correspondingly large value of R2.

False

In multiple linear regression if SSR = SST then the value of R2 is zero.

False

In a multiple regression application, the least important variable in the model is the one with the smallest (in absolute value) estimated coefficient, bj.

False

In selecting multiple regression model, the full model, which includes all of the predictor variables, will always have the largest value of R2.

True