Chapter 9 Multiple Regression 361Coeffi cients and the Prediction Equation
At this point you know the model is statistically signifi cant and accounts for
about 37% of the variability in calculus scores. What is the regression equa-
tion itself and which predictor variables are most important?
You can read the estimated regression model from cells A16:I23, shown
in Figure 9-5, where the first column contains labels for the predictor
variables.The Coeffi cients column (B16:B23) gives the estimated coeffi cients for the
model. The corresponding prediction equation is
Calc 5 27.943 1 7.192 1 Calc HS 21 0.352 1 ACT Math 21 0.827 1 Alg Place 2
1 3.683 1 Alg2 Grade 21 0.111 1 HS Rank 21 2.627 1 Gender Code 2
The coeffi cient for each variable estimates how much the calculus score
will change if the variable is increased by 1 and the other variables are held
constant. For example, the coeffi cient 0.352 of ACT Math indicates that the
calculus score should increase by 0.352 point if the ACT math score in-
creases by 1 point and all other variables are held constant.
Some variables, such as Calc HS, have a value of either 0 or 1, in this
case to indicate the absence or presence of calculus in high school. The co-
effi cient 7.192 is the estimated effect on the calculus score of taking high
school calculus, other things being equal. Because 10 points correspond to
one letter grade, the coeffi cient 7.192 for Calc HS is almost one letter grade.
Using the coeffi cients of this regression equation, you can forecast what
a particular student’s calculus score may be, given background information
on the student. For example, consider a male student who did not take cal-
culus in high school, scored 30 on his ACT Math exam, scored 23 on his
algebra placement test, had a 4.0 grade in second-year high school algebra,
and was ranked in the 90th percentile in his high school graduation class.
You would predict that his calculus score would be
Calc 5 27.943 1 7.192 1021 0.352 13021 0.827 12321 3.683 1 4.0 21 0.111^19021 2.627^1125 74.87, or about 75 pointsFigure 9-5
Parameter
estimates
and p values