Download Prediction

Agenda
1.Exam 2 Review
2.Regression
a.Prediction
b.Polynomial Regression
Prediction
 One of the objectives of regression was to
be able to predict the behavior of the
dependent variable.
 Prediction:
Providing estimates of values of the
dependent variable by using the
explanatory regression equation:
Ŷ  b0  b1X
OR:
yˆ  b0  b1x1  b2 x2  b3 x3  ...  bk xk
Prediction (cont.)
 First need to establish that the model is a
good model with strong explanatory
power.
 We can only use prediction in the region
of the data used in the estimation
process.
 Replace X in the equation with the value
for which you want to predict the
dependent variable.
Example #1:
The regression model:
Y = 71 + 10 X
1. Is the relationship between X and Y positive or
negative?
2. If X is 9, what is y?
3. If X changes one unit, how much does Y
change?
4. If X is 0, what is y?
Example #2:
Y = -.869 + .0611 X1 + .923 X2
where X1 is miles driven, X2 is no of deliveries
and Y is hours of drive time.
1. Predict the total drive time of a driver who
needs to make 3 deliveries and travel 70 miles.
2. Predict the total drive time of a drive who
still drives 70 miles but now makes 4 deliveries?
Polynomial Regression
 If the relationship between the dependent and an
independent variable is not linear, but curvilinear,
then using polynomials may improve the model.
Y=0+1 X + 2X2 + 3X3 +. . . + mXm
Y
Y
Ŷ  b  b X
0 1
Ŷ  b  b X
0 1
Ŷ  b  b X  b X 2
0 1
2
(b  0)
2
Ŷ  b  b X  b X2  b X3
0 1
2
3
X1
X1
Polynomial Regression Example
The polynomial regression equation is:
SALES = 3.52 + 2.51 ADVERT - 0.0875 ADV2
Predictor
Constant
ADVERT
ADV2
Coef
3.5150
2.5148
-0.08745
R-sq = 95.9%
Analysis of Variance:
SOURCE
DF
Regression
2
Error
18
Total
20
Stdev
0.7385
0.2580
0.01658
t-ratio
4.76
9.75
-5.28
p
0.000
0.000
0.000
R-sq(adj) = 95.4%
SS
630.26
27.14
657.40
MS
315.13
1.51
F
208.99
p
0.000
Polynomial Regression (cont.)
SALES = 3.52 + 2.51 ADVERT - 0.0875 ADV2
1.
Test whether or not the coefficient for ADV2 is significant.
2.
Predict what sales will be when advertising is
7 (in thousands).
3.
Predict what sales will be when advertising is
15 (in thousands).
4.
Predict what sales will be when advertising is
23 (in thousands).