Problem 2
The formula for a regression equation is \(Y^{\prime}=2 X+9\). a. What would be the predicted score for a person scoring 6 on \(\mathrm{X} ?\) b. If someone's predicted score was \(14,\) what was this person's score on \(X ?\)
Problem 4
What does the standard error of the estimate measure? What is the formula for the standard error of the estimate?
Problem 5
a. In a regression analysis, the sum of squares for the predicted scores is 100 and the sum of squares error is \(200,\) what is \(\mathrm{R} 2 ?\) b. In a different regression analysis, \(40 \%\) of the variance was explained. The sum of squares total is 1000 . What is the sum of squares of the predicted values?
Problem 6
For the X,Y data below, compute: a. \(\mathrm{r}\) and determine if it is significantly different from zero. b. the slope of the regression line and test if it differs significantly from zero. c. the \(95 \%\) confidence interval for the slope. $$ \begin{array}{|l|l|} \hline X & Y \\ \hline 4 & 6 \\ \hline 3 & 7 \\ \hline 5 & 12 \\ \hline 11 & 17 \\ \hline 10 & 9 \\ \hline 14 & 21 \\ \hline \end{array} $$
Problem 7
What assumptions are needed to calculate the various inferential statistics of linear regression?
Problem 9
A sample of \(X\) and \(Y\) scores is taken, and a regression line is used to predict \(Y\) from \(X .\) If \(S S Y^{\prime}=300, S S E=500,\) and \(N=50,\) what is: (a) SSY? (b) the standard error of the estimate? (c) \(\mathrm{R}^{2} ?\)
Problem 11
The equation for a regression line predicting the number of hours of TV watched by children (Y) from the number of hours of TV watched by their parents \((\mathrm{X})\) is \(\mathrm{Y}^{\prime}=4+1.2 \mathrm{X} .\) The sample size is 12 . a. If the standard error of \(\mathrm{b}\) is \(.4,\) is the slope statistically significant at the .05 level? b. If the mean of \(X\) is \(8,\) what is the mean of \(Y ?\)
Problem 12
Based on the table below, compute the regression line that predicts \(Y\) from \(X\). $$ \begin{array}{|c|c|c|c|c|} \hline \mathbf{M}_{\mathrm{x}} & \mathrm{M}_{\mathrm{Y}} & \mathrm{s}_{\mathrm{x}} & \mathrm{S}_{\mathrm{Y}} & \mathrm{r} \\ \hline 10 & 12 & 2.5 & 3.0 & -0.6 \\ \hline \end{array} $$
Problem 14
True/false: If the slope of a simple linear regression line is statistically significant, then the correlation will also always be significant.
Problem 16
True/false: If the correlation is \(.8,\) then \(40 \%\) of the variance is explained.
