Linear Regression Examples

Examples 1 and 2 are by courtesy of Dr. Elton Lacey, 142 Class Notes, 1995.

1. The price of a pair of tickets to a college's home football games is given in the table below.

Year | 1977 1979 1981 1983 1985 1987 1989 1991

$ Price | 8 9 10 12 13 15 16 18

Find the least squares regression line for the price as a function of the number of years past 1977.

Observe r^2 and the graph. What doe the line predict for the price in the year 1995?

2. The chart below gives the average weight of the brain as a percentage of body weight at different ages.

Age 0 2 4 6 8 10 12 14 16

11 8 7 6 5 4.5 4 3.5 3.25

Find the least squares linear regression for the %brain wt. as a function of age, observe the graph and r^2.

3. Humiture is a measure of our stress and discomfort at different temperatures and humidities. In the data set, X is the humidity in percent form and y is the humiture if the temperature is 100 degrees Farenheit.

X 10 20 30 40 50 60

Y 85 92 99 105 111 118

a) Find the least squares regression line and predict the humiture for 100 degrees Farenheit and 70% humidity.

b) If the humidity increases by 5%, the humiture increases by _____ when the temperature is 100 degrees.

The second data set is for 90 degrees Farenheit. Do a and b for this data.

X 10 20 30 40 50 60

Y 73 79 84 88 93 97