This problem is based on problems 18.1, 18.2, 18.9, & 18.10 from Lomax & Hahs-Vaughn, 3rd ed. You are given the following data, where X1(GRE total score) and X2 (undergraduate GPA) are used to predict Y (graduate GPA): Y X1 X2 3.4 95 3 3.2 125 2.8 3.9 120 3.7 3.3 115 2.7 3.6 110 3.5 3.2 135 3.5 4 145 3.2 Determine the following multiple regression values. Report intercept and slopes for regression equation accurate to 3 decimal places: Intercept: a= Partial slope X1: b1= Partial slope X2: b2= Report sum of squares and coefficient of multiple determination accurate to 3 decimal places: R2= SSTotal= 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= Report the standard error of the partial slope estimate for GRE total along with the test statistic (report answers accurate to 3 decimal places): s(b1)= t1=
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.
This problem is based on problems 18.1, 18.2, 18.9, & 18.10 from Lomax & Hahs-Vaughn, 3rd ed.
You are given the following data, where X1(GRE total score) and X2 (undergraduate GPA) are used to predict Y (graduate GPA):
| Y | X1 | X2 |
|---|---|---|
| 3.4 | 95 | 3 |
| 3.2 | 125 | 2.8 |
| 3.9 | 120 | 3.7 |
| 3.3 | 115 | 2.7 |
| 3.6 | 110 | 3.5 |
| 3.2 | 135 | 3.5 |
| 4 | 145 | 3.2 |
Determine the following multiple regression values.
Report intercept and slopes for regression equation accurate to 3 decimal places:
Intercept: a=
Partial slope X1: b1=
Partial slope X2: b2=
Report sum of squares and coefficient of multiple determination accurate to 3 decimal places:
R2=
SSTotal=
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=
Report the standard error of the partial slope estimate for GRE total along with the test statistic (report answers accurate to 3 decimal places):
s(b1)=
t1=
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