1.   A mathematics teacher recorded the length of time (x) hours studied with the obtained score, (y) from eight selected students. The data are summarised as follows.

a.    Calculate the value of the correlation coefficient for these data.

b.    Calculate and interpret the determination value.

2.   The table below gives information on GPAs and starting salaries (rounded in the nearest thousand ringgit) of seven college graduates.

a.    Determine the independent (x) and dependent (y) variables.

b.    Draw the scatter plot.

c.    Compute the value of the correlation coefficient.

d.    Determine the regression line equation.

e.    Plot the regression line on the scatter plot if appropriate.

f.   Construct a 95% confidence interval for B.

g.   Test whether B is different from zero at a 1% significance level.

3.    Some of the regression output is provided below. Let x = house size and y=selling price.

a.    Give the value of r2  and interpret it in the problem context.

b.   Give the least square regression equation for predicting price from house size.

c.    What is the estimated change in the average selling price of a house for an increase in house size of 100 square feet?

d.    Predict the price for the 60th  observed house, which had a home size of 2430 square feet.

e.    Write the null and alternative hypotheses for assessing if B is positive?.

f.     Report the corresponding p-value and state the conclusion in the context of this problem.

4.     Following are the data on total hours studied over two weeks and test scores at the two weeks.

a.    Decide at a 1% significance level whether the data provide sufficient evidence to conclude that the total hours studied are useful for predicting the test score.

b.    Find and interpret a 99% confidence interval for the slope of the population regression line that relates the test score to the total hours studied.

5. A simple regression model contains:

a. two independent variables

b. two dependent variables

c. one independent and one dependent variable

d. more than one independent variable

6. A linear regression:

a. gives a straight– line relationship between two variables

b. gives a relationship between two variables that is not of a straight line

c. gives a straight– line relationship between three variables

d. contains only two variables

7. In a regression model, the y– intercept is:

a. the point where the y–axis intersects the x–axis

b. the point where the regression line intersects the y–axis

c. the point where the x–axis intersects the y–axis

d. the value of y when x is equal to 1

8. In a regression model, the slope represents:

a. the point where the y–axis intersects the x–axis

b. the change in y due to a one– unit change in x

c. the point where the x–axis intersects the y–axis

d. the change in the independent variable due to a one– unit change in the dependent variable

9. In the regression model y = A + Bx + ε , A and B are called:

a. the sample statistics

b. the random variables

c. the population parameters

d. the omitted variables

10. A scatter diagram is obtained by:

a. scattering the values of x over the values of y

b. scattering the values of y over the values of x

c. plotting the paired values of x and y

d. plotting the values of A and B

11. For a regression model, the error sum of squares, denoted by SSE, is equal to the sum of: