You are given the following data, where X1X1 (GRE total score) and X2X2 (undergraduate GPA) are used to predict YY (graduate GPA): YY X1X1 X2X2 3.3 115 2.7 4 130 2.6 3.2 125 2.8 3.1 90 2.8 3.2 135 3.5 3.8 125 3.6 3.2 105 3.1 3.6 110 3.5
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.
You are given the following data, where X1X1 (GRE total score) and X2X2 (undergraduate GPA) are used to predict YY (graduate GPA):
| YY | X1X1 | X2X2 |
|---|---|---|
| 3.3 | 115 | 2.7 |
| 4 | 130 | 2.6 |
| 3.2 | 125 | 2.8 |
| 3.1 | 90 | 2.8 |
| 3.2 | 135 | 3.5 |
| 3.8 | 125 | 3.6 |
| 3.2 | 105 | 3.1 |
| 3.6 | 110 | 3.5 |
Report intercept and slopes for regression equation accurate to 3 decimal places:
Intercept: a=a=
Partial slope X1X1: b1=b1=
Partial slope X2X2: b2=b2=
Report sum of squares accurate to 3 decimal places:
SSreg=SSreg=
SSres=SSres=
Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
F-ratio =
P-value =
Report the variance of the residuals accurate to 3 decimal places:
MSres=MSres=
Report the standard error of the partial slope estimate for undergraduate GPA along with the test statistic (report answers accurate to 3 decimal places):
s(b2)=s(b2)=
t2=t2=
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