A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. Lovers 4 8 3 7 0 6 5 6 GPA 2.7 2.3 3.4 2.4 3.5 2.9 2.7 2.8
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 study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below.
| Lovers | 4 | 8 | 3 | 7 | 0 | 6 | 5 | 6 |
|---|---|---|---|---|---|---|---|---|
| GPA | 2.7 | 2.3 | 3.4 | 2.4 | 3.5 | 2.9 | 2.7 | 2.8 |
r2r2 = (Round to two decimal places)
Interpret r2r2 :
- There is a large variation in students' GPAs, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 80%.
- Given any group of students who have all had the same number of lovers, 80% of all of these studetns will have the predicted GPA.
- 80% of all students will have the average GPA.
- There is a 80% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had.
The equation of the linear regression line is:
ˆyy^ = + xx (Please show your answers to two decimal places)
Use the model to predict the GPA of a college student who as had 7 lovers.
GPA = (Please round your answer to one decimal place.)
Interpret the slope of the regression line in the context of the question:
- The slope has no practical meaning since a GPA cannot be negative.
- For every additional lover students have, their GPA tends to decrease by 0.15.
- As x goes up, y goes down.
Interpret the y-intercept in the context of the question:
- If a student has never had a lover, then that student's GPA will be 3.57.
- The best prediction for the GPA of a student who has never had a lover is 3.57.
- The y-intercept has no practical meaning for this study.
- The average GPA for all students is predicted to be 3.57.
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