1. What are multivariate statistical techniques?

2. What is correlation analysis?

3. What is the Pearson's r correlation coefficient and how do you calculate it? (Provide an explanation and give a formula.)

4. Table 1 contains data on the difference between urban and suburban nighttime temperatures for a set of US cities. The table also contains data on their population size. (For this problem, designate population as X and nighttime difference as Y)

Table: Temperature Difference and Population Data

City Population(millions) Temp Diff

New York, NY 19.8 8

Los Angeles, CA 12.7 9

Chicago, IL 9.3 1

Dallas, TX 5.5 5

Miami, FL 5.2 -2

Washington, DC 5.0 4

Houston, TX 5.0 1

Philadelphia, PA 4.5 8

Atlanta, GA 4.5 3

Detroit, MI 4.5 6

Boston, MA 4.4 5

Riverside, CA 3.5 4

Phoenix, AZ 3.5 5

Seattle, WA 3.1 5

a. Just by looking at the scatterplot above, what can you say about the: (each one of these points)

i. Direction of the relationship

ii. Form of the relationship

iii. Degree or strength of the relationship

b. Calculate Pearson's r correlation coefficient.

5. A researcher investigates the relationship between pollution levels (CO, measured in ppm of CO) and distance from major intersections (DIST, straight line distance, measured in meters). Using 102 data points distributed throughout the city she finds a correlation of r= -0.32.

a. Test the hypothesis that there is no correlation between pollution levels (CO) and distance from major intersections (DIST). Use a significance level of 0.05. Remember to follow all the steps and show your work (define the null and alternative hypothesis, calculate your statistic, find your critical value, decide whether to reject or not the null hypothesis).

b. Test the hypothesis that there is a negative relationship between pollution levels and distance from major intersections. Use a significance level of 0.05. Remember to follow all the steps and show your work (define the null and alternative hypothesis, calculate your statistic, find your critical value, decide whether to reject or not the null hypothesis).

c. When the researcher estimates a regression model of CO pollution levels as a function of distance (DIST) measured in meters to major intersections, she obtains the following result:CO = 12 - 0.005*DIST

i. What is the estimated CO pollution in the middle of an intersection (i.e. DIST=0)?

ii. What is the estimated CO pollution at a location that is 800 meters away from a major intersection?