Correlation and Regression-
1. A study is done to see whether there is a relationship between a student's GPA and the number of hours the student studies per week. The data is as follows.
Hours, x 3 12 9 15 5 7 16
GPA, y 2.1 3.5 3.0 4.0 1.7 3.2 3.7
(a) Draw a scatter plot.
(b) Compute the value of the correlation coefficient r.
(c) Test the significance of the correlation coefficient at α = .01
(d) Find the equation for the least squares line.
(e) Graph the least squares line on your scatter plot.
2. Does the weight of a vehicle affect gas mileage? The following random sample was collected where x = weight of a vehicle in hundreds of pounds and y = miles per gallon.
x 26 35 29 39 20
y 22.0 16.1 18.8 15.7 23.4
a) Create a scatter plot for this data.
b) Compute the coefficient of correlation.
c) Test the significance of the correlation coefficient at α = .05.
d) Find the equation for the least squares line.
e) If the weight of a vehicle is 32, what do you predict the gas mileage will be?
3. An emergency service wishes to see whether a relationship exists between the outside temperature and the number of emergency calls it receives for a 7-hour period. The data is given below.
Temperature x 68 74 82 88 93 99 101
Number of calls, y 7 4 8 10 11 9 13
a) Create a scatter plot for this data.
b) Compute the coefficient of correlation. You may use the following sums.
Σx = 605 Σy = 62 Σxy = 5,535 Σx2 = 53,219 Σy2 = 600.
c) Test the significance of the correlation coefficient at α = .05.
d) Find the equation for the least squares line.
e) If the temperature is 85, what do you predict the number of calls will be?
f) What percent of the variation in y is captured by the model?