Description: Ice cream consumption was measured over 30 four-week periods from March 18, 1951 to July
11, 1953. The purpose of the study was to determine if ice cream consumption depends on price or
temperature.
Number of cases: 30
Variable Names:
1. Date: Time period (1-30) of the study (from 3/18/51 to 7/11/53)
2. IC: Ice cream consumption in pints per person
3. Price: Price of ice cream per pint in dollars
4. Temp: Average monthly temperature in degrees F. (tempsq is temp squared)
A sample of the data:
date
IC
1
.386
2
.374
3
.393
4
.425
price
.270
.282
.277
.280
temp
41
56
63
68
Three regressions were run on the data:
The first regression equation is
IC = 0.923 - 2.05 price
Predictor
Constant
price
s = 0.06466
Coef
0.9230
-2.047
Stdev
0.3964
1.439
R-sq = 6.7%
t-ratio
p
2.33 0.027
-1.42 0.166
R-sq(adj) = 3.4%
The second regression equation is
IC = 0.597 - 1.40 price + 0.00303 temp
Predictor
Coef
Stdev
Constant
0.5966
0.2583
price
-1.4018
0.9251
temp
0.0030303 0.0004700
s = 0.04132
R-sq = 63.3%
t-ratio
p
2.31 0.029
-1.52 0.141
6.45 0.000
R-sq(adj) = 60.6%
IC = 0.597 - 1.40 price + 0.00303 temp -.000004tempsq
Predictor
Coef
Stdev
t-ratio
p
Constant
0.5966
0.2583
2.31 0.029
price
-1.4018
0.9251
-1.52 0.141
temp
0.0030303 0.0004700
6.45 0.000
Ttemsq
-.000004 .005
.0008 .890
s = 0.04132 R-sq = 64.3% R-sq(adj) = 60.1%
Which model will give better predictions? Explain your answer.
Interpret each of the coefficients for the better of the two models.
Using the best model, what is the true relationship between price and ice cream consumption and between
temperature and ice cream consumption?
Interpret the relationship between temp and IC for the third model
Can we be 90 percent sure that a lower price will increase ice cream consumption?
How much Ice cream will be consumed if the price is .28 and the temperature is 60 degrees?
How much will be consumed if the price is .28 and the temperature was 180 degrees?