Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes. Brand Weight Price ($) A 17.8 2,100 B 16.1 6,350 C 14.9 8,370 D 15.9 6,200 E 17.2 4,000 F 13.1 8,600 G 16.2 6,000 H 17.1 2,480 I 17.6 3,400 J 14.1 8,000 These data provided the estimated regression equation ŷ = 28,648 − 1,444x. For these data, SSE = 7,568,661.27 and SST = 52,874,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance.
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.
| Brand | Weight | Price ($) |
|---|---|---|
| A | 17.8 | 2,100 |
| B | 16.1 | 6,350 |
| C | 14.9 | 8,370 |
| D | 15.9 | 6,200 |
| E | 17.2 | 4,000 |
| F | 13.1 | 8,600 |
| G | 16.2 | 6,000 |
| H | 17.1 | 2,480 |
| I | 17.6 | 3,400 |
| J | 14.1 | 8,000 |
Ha: ?1 ≠ 0
Ha: ?1 = 0
Ha: ?1 < 0
Ha: ?0 = 0
Ha: ?0 ≠ 0
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