How is a linear relationship between two variables measured in statistics? Explain. ? ? 2. What is the symbol for t

Bus 302 Quiz Part 2 Revised                          Name: _______________

Week 4

Respond to each of the following short answer questions:

1. How is a linear relationship between two variables measured in statistics? Explain.

2. What is the symbol for the sample correlation coefficient? The population correlation coefficient?

3. What is the range of values for the correlation coefficient?

4. What is the general form for the regression line used in statistics?

5. What is meant by the “line of best fit”?

6. When all the points fall on the regression line, what is the value of the correlation coefficient?

7. Explain the differences between the explained variation and the unexplained variation.

In the following problem (# 8 below) perform the following steps.

8. Problem: Forest Fires and Acres Burned SHOW YOUR WORK

An environmentalist wants to determine the relationships between the numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned. The data for 8 recent years are shown.

Fires x │  72  69  58  47  84  62  57  45

Acres y │ 62  42  19  26  51  15  30  15

            a. Draw the scatter plot for the variables.

            b. Compute the value of the correlation coefficient and identify the line of best fit (y’ = a + bx) with the specific values for a and b from the problem below.

            c. State the hypotheses.

            d. Test the significance of the correlation coefficient at  = 0.05. Using Table I or the P-value method.

            e. Give a brief explanation of the type of relationship. Assume all assumptions have been met.

         f. Find y’ when x = 60 fires.