To Lecture Notes

IT 223 -- 2/7/11

Review Questions

1. If x = 5, y = 3, SD_x = 0.5, SD_y = 2, and r = 0.75, compute the regression line.

   Ans: The regression line is

   y - 3 = (0.75 * 2 / 0.5) (x - 5)

   y - 3 = 3 (x - 5)

   y = 3 x - 12

2. What does y^ (read y hat) mean?

   Ans: y^ means the predicted value using the regression equation for a given x:

   y^ = ax + b

   y_i^ means the predicted value for the x-value x_i.

3. Using the regression line in Question 4, what is y^ if x = 4.

   Ans: y^{^} = 3 x - 12 = 3 * 4 - 12 = 0.0

4. For a bivariate dataset, if the x-variable is 2 SD_xs above x, how many SD_ys above y will y^ be?

   Ans: 2 × SD^y × r above the y mean.

5. What four things must a regression model satisfy to be considered a good regression model?

   Ans: (1) High R-squared value, (2) unbiased residuals in residual plot, (3) homoscedastic residuals in residual plot.

6. Use SPSS to compute the regression equation for the Hamster Dataset. Is the regression model a good one?

   Ans: R-squared is 0.275, which is a little low for biology. The regression equation is

   Lifetime = 0.015 * Hiber + 0.797

   The residual plot shows that the residuals are unbiased and homoscedastic. The normal plot of the residuals shows that they are fairly normally distributed, slightly skewed to the left.

More about Correlations

• See the Cautions Section in Linear Correlation

• The r-squared value r² measured the proportion of variation in the dependent variable that can be attributed to the independent variable.

• Correlation does not always imply causation.

• Correlation does not indicate the strength of a nonlinear relationship.

• Outliers can distort the correlation. They usually make it smaller.

Review for Midterm

• Look at the Midterm Review Guide and sample midterms on the ExamInfo Page.