a. Compute the percentage of variation in the commercial cost which is explained by the variation in the Nielsen Rating. b. Write down the analysis of variance table for the regression of
A study was undertaken to relate the cost of television commercials to the characteristics of the television programs in 2008. Data were collected on the following variables for 45 different television programs:
Y = Cost of airing a 30 second commercial for a television program (IN THOUSANDS OF DOLLARS)
X1 = Nielsen Rating of the program (percentage of television sets tuned to the program).
X2 = Percentage of the audience consisting of the 18-34 age group watching the program.
X3 = 1 If the program is on primetime.
0 If the program is not on prime time.
X4 = 1 If the program is a comedyprogram.
0 If the program is not a comedy program.
NOTE OF INTEREST: A Nielsen Rating of 1 would mean that 1,128,000
households were tuned in to that program in 2008.
As an example: one of the television programs in the sample was “Desperate Housewives”. It had a Nielsen Rating of 3.2, it was shown in prime time, it was not a comedy program, 42% of the audience consisted of the 18-34 age group, and the cost of a 30 second Commercial was $210,000. For this program:
Y = 210
X1 = 3.2
X2 = 42
X3 = 1
X4 = 0
The correlation matrix is:
| X1 | X2 | X3 | X4 | ||
| X1 | 0.715 | ||||
| X2 | 0.345 | 0.341 | |||
| X3 | 0.561 | 0.403 | 0.316 | ||
| X4 | -0.232 | 0.127 | -0.187 | -0.225 |
The results on the regression of Y on X1, X2, X3 and X4 are asfollows:
| Variable | Regression Coefficient | Standard Error |
| Constant | 15 | 2.53 |
| X1 | 32 | 4.82 |
| X2 | 1.10 | 0.35 |
| X3 | 25 | 6.54 |
| X4 | 10 | 7.79 |
SST = 1,125,000
SSE= 215,640
The results on the regression of Y on X1, X2, and X3 are as follows:
| Variable | Regression Coefficient | Standard Error |
| Constant | 20 | 2.10 |
| X1 | 37 | 3.67 |
| X2 | 1.20 | 0.32 |
| X3 | 30 | 5.00 |
SST = 1,125,000
SSE= 224,516
The Nielsen Ratings for the 45 programs sampled varied from a low of 0.8 to a high of 15.6. Plots of the standardized residuals versus other variables appeared to be random for both of the above regressions.
Compute the percentage of variation in the commercial cost which is explained by the variation in the Nielsen Rating.
Write down the analysis of variance table for the regression of Y on X1, X2, X3. and X4. Using it and any other information provided above, test for the statistical significance of the overall regression equation and determine which variables should be included and which variables should be deleted (if any). In your answer, state the null hypothesis and alternate hypothesis of all tests performed, compute the test statistics and explain how you arrive at your conclusions (use the attached statistical tables).
For the regression model selected, compute the coefficient of determination and interpret this measure with respect to this application. Be specific in your interpretation.
Obtain a 95% prediction interval for the cost of a 30 second commercial for the prime time comedy program “TWO AND A HALF MEN”. This program has a Nielsen rating of 5.9 and 80% of the audience is in the 18-34 age range.
The non comedy television program, "NCIS", has a rating of 8.2 and 30% of the audience is in the 18-34 age range. The comedy television program "TWO AND A HALF MEN", has a rating of 5.9 and 80% of the audience is in the 18-34 age range. What is the estimated difference in the cost of a 30 second commercial for these two programs (both of these programs are shown during prime time).
Estimate the 25th percentile of the cost of a 30 second commercial for a non comedy prime time program with a Nielsen Rating of 5.0 and with 60% of the audience in the 18-34 age range.
