A market researcher is studying on-line subscription services. She is particularly interested in what variables relate to the number of subscriptions for a particular on-line service. She is able to obtain the following sample information on 25 on-line subscription services. The following notation is used: Sub = Number of subscriptions (in thousands) Web page hits = Average monthly count (in thousands) Adv = The advertising budget of the service (in $ hundreds) Price = Average monthly subscription price ($) Service Subscriptions Web Page Hits Adv Price 1 37.95 588.9 13.2 35.1 2 37.66 585.3 13.2 34.7 3 37.55 566.3 19.8 34.8 4 38.78 642.9 17.6 35.1 5 37.67 624.2 17.6 34.6 6 38.23 603.9 15.4 34.8 7 36.9 571.9 11.0 34.7 8 38.28 584.3 28.6 35.3 9 38.95 605.0 28.6 35.1 10 39.27 676.3 17.6 35.6 11 38.3 587.4 17.6 34.9 12 38.84 576.4 22.0 35.4 13 38.14 570.8 17.6 35 14 38.39 586.5 15.4 35.5 15 37.29 544.0 11.0 34.9 16 39.15 611.1 24.2 35 17 38.29 643.3 17.6 35.3 18 38.09 635.6 19.8 34.8 19 37.83 598.9 15.4 35.1 20 39.37 657.0 22.0 35.3 21 37.81 595.2 15.4 35.1 22 37.42 520.0 19.8 35.1 23 38.83 629.6 22.0 35.3 24 38.33 680.0 24.2 34.7 25 40.24 651.2 33.0 35.8 GIVEN: Determine the regression equation: y^ = -5.7328 + 0.0075 x1 + 0.0509 x2 + 1.0974 x3 FIND: H0: β1 = β2 = β3 = 0 H1: Not all βi's = zero. Reject H0 if F > F = 35.38
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A market researcher is studying on-line subscription services. She is particularly interested in what variables relate to the number of subscriptions for a particular on-line service. She is able to obtain the following sample information on 25 on-line subscription services. The following notation is used:
Sub = Number of subscriptions (in thousands)
Web page hits = Average monthly count (in thousands)
Adv = The advertising budget of the service (in $ hundreds)
Price = Average monthly subscription price ($)
| Service | Subscriptions | Web Page Hits | Adv | Price |
| 1 | 37.95 | 588.9 | 13.2 | 35.1 |
| 2 | 37.66 | 585.3 | 13.2 | 34.7 |
| 3 | 37.55 | 566.3 | 19.8 | 34.8 |
| 4 | 38.78 | 642.9 | 17.6 | 35.1 |
| 5 | 37.67 | 624.2 | 17.6 | 34.6 |
| 6 | 38.23 | 603.9 | 15.4 | 34.8 |
| 7 | 36.9 | 571.9 | 11.0 | 34.7 |
| 8 | 38.28 | 584.3 | 28.6 | 35.3 |
| 9 | 38.95 | 605.0 | 28.6 | 35.1 |
| 10 | 39.27 | 676.3 | 17.6 | 35.6 |
| 11 | 38.3 | 587.4 | 17.6 | 34.9 |
| 12 | 38.84 | 576.4 | 22.0 | 35.4 |
| 13 | 38.14 | 570.8 | 17.6 | 35 |
| 14 | 38.39 | 586.5 | 15.4 | 35.5 |
| 15 | 37.29 | 544.0 | 11.0 | 34.9 |
| 16 | 39.15 | 611.1 | 24.2 | 35 |
| 17 | 38.29 | 643.3 | 17.6 | 35.3 |
| 18 | 38.09 | 635.6 | 19.8 | 34.8 |
| 19 | 37.83 | 598.9 | 15.4 | 35.1 |
| 20 | 39.37 | 657.0 | 22.0 | 35.3 |
| 21 | 37.81 | 595.2 | 15.4 | 35.1 |
| 22 | 37.42 | 520.0 | 19.8 | 35.1 |
| 23 | 38.83 | 629.6 | 22.0 | 35.3 |
| 24 | 38.33 | 680.0 | 24.2 | 34.7 |
| 25 | 40.24 | 651.2 | 33.0 | 35.8 |
GIVEN:
- Determine the regression equation: y^ = -5.7328 + 0.0075 x1 + 0.0509 x2 + 1.0974 x3
FIND:
H0: β1 = β2 = β3 = 0
H1: Not all βi's = zero.
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