Story Name: Ice Cream Consumption

Abstract: 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 the variables price, income, or temperature. The variables
Lag-temp and Year have been added to the original data.

Create a scatterplot of the variable IC plotted against Date. This plot
shows that ice cream consumption has a seasonal cycle. There also appears to be a
gradually increasing trend in ice cream consumption from year to year. This is
time series data, and the assumption that the errors of any ordinary regression
model are independent will probably be violated.

The original study concluded that of the three possible predictor variables,
Price, Income, and Temp, only Temp had a significant effect on the dependent
variable IC. However, this study did not include the variable Year.

Velleman (1995) reanalyzed these data and determined that the model including the
predictors Lag-temp (Temp lagged by one time period) and Year were significant
predictors of ice cream consumption. Figure 2 shows a plot of IC vs. Lag-temp
colored by Year with individual regression lines superimposed for each year.
Since the variable Lag-temp varies with the season, including it in the model
corrects most of the problems of autocorrelation among the errors. Figure 3 shows
the results of the linear model predicting IC by Lag-temp and Year. Note the
positive effect of Year and Lag-temp and the high adjusted R-square of 85.1%.

Reference: Koteswara Rao Kadiyala (1970) Testing for the independence of
regression disturbances. Econometrica, 38, 97-117. Also found in: Hand, D.J., et
al. (1994) A Handbook of Small Data Sets, London: Chapman & Hall, 214.
Authorization: Contact Author 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 the variables
price, income, or temperature. The variables Lag-temp and Year have been added to
the original data. 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 capita
3.Price: Price of ice cream per pint in dollars
4.Income: Weekly family income in dollars
5.Temp: Mean temperature in degrees F.
6.Lag-temp: Temp variable lagged by one time period
7.Year: Year within the study (0 = 1951, 1 = 1952, 2 = 1953)

The Data:

date IC price income temp Lag-temp Year
1 .386 .270 78 41 56 0
2 .374 .282 79 56 63 0
3 .393 .277 81 63 68 0
4 .425 .280 80 68 69 0
5 .406 .272 76 69 65 0
6 .344 .262 78 65 61 0
7 .327 .275 82 61 47 0
8 .288 .267 79 47 32 0
9 .269 .265 76 32 24 0
10 .256 .277 79 24 28 0
11 .286 .282 82 28 26 1
12 .298 .270 85 26 32 1
13 .329 .272 86 32 40 1
14 .318 .287 83 40 55 1
15 .381 .277 84 55 63 1
16 .381 .287 82 63 72 1
17 .470 .280 80 72 72 1
18 .443 .277 78 72 67 1
19 .386 .277 84 67 60 1
20 .342 .277 86 60 44 1
21 .319 .292 85 44 40 1
22 .307 .287 87 40 32 1
23 .284 .277 94 32 27 1
24 .326 .285 92 27 28 2
25 .309 .282 95 28 33 2
26 .359 .265 96 33 41 2
27 .376 .265 94 41 52 2
28 .416 .265 96 52 64 2
29 .437 .268 91 64 71 2
30 .548 .260 90 71 ¥ 2