Statistics Name: __________________

Least-squares regression lines and prediction

1. The Sanchez household is about to install solar panels to reduce the cost of heating their house. In order to know how much the solar panels help, they record their consumption of natural gas before the panels are installed.

A heating degree-day is the usual measure of demand for heating. One degree-day is accumulated for each degree a day’s average temperature falls below 65°F. An average temperature of 20°F, for example, corresponds to 45 degree-days.

A B C123456789

1 01 11 21 31 41 51 61 7

Month Degree-daysGas (100 cubic ft)November 24 6.3December 51 10.9January 43 8.9February 33 7.5March 26 5.3Apri l 13 4.0May 4 1.7June 0 1.2July 0 1.2August 1 1.2September 6 2.1October 12 3.1November 30 6.4December 32 7.2January 52 11.0February 30 6.9

a) On graph paper, make a scatterplot of the data. Think carefully about which you choose as the explanatory and the response variables.

b) Describe the association of the variables. What does this mean in real terms?

c) Enter the data on your calculator and calculate r: _____________

d) Find the equation of the least-squares regression line: __________________and graph it on your scatterplot.

e) The Sanchez family wants to use this relationship to predict their natural gas consumption. If a month averages 20 degree-days per month (45°F), how much gas can they expect to use in that month?

2. Five-year old Susie’s parents are concerned that she seems short for her age. Their doctor has the following record of Susie’s height:

age (months): 36 48 51 54 57 60height (cm): 86 90 91 93 94 95

a) Make a scatterplot of these data on graph paper.

b) Find the equation of the least-squares regression line of height on age.

c) Sketch the regression line on your scatterplot.

d) Predict Susie’s height at 60 months and 80 months.

e) Predict Susie’s height at 480 months! How old is this ? What is this height in feet and inches ?

3. Match the following scatterplots with their regression equations and correlations.