A statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of the number of these problems completed during the course of the semester. Problems 51 58 62 65 68 76 77 84 85 91 Course Grade 62 68 66 66 67 72 73 73 76 75 Determine the following: Pearson Correlation coefficient r Least square regression line SSE Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE. Y X1 X2 1 40 25 2 45 20 1 38 30 3 50 30 2 48 28 3 55 30 3 53 34 4 55 36 4 58 32 3 40 34 5 55 38 3 48 28 3 45 30 2 55 36 4 60 34 5 60 38 5 60 42 5 65 38 4 50 34 3 58 38 Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.
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 statistics instructor at a large western university would like to examine the relationship (if any) between the number of optional homework problems students do during the semester and their final course grade. She randomly selects 12 students for study and asks them to keep track of the number of these problems completed during the course of the semester.
|
Problems |
51 |
58 |
62 |
65 |
68 |
76 |
77 |
84 |
85 |
91 |
|
Course Grade |
62 |
68 |
66 |
66 |
67 |
72 |
73 |
73 |
76 |
75 |
Determine the following:
- Pearson
Correlation coefficient r - Least square regression line
- SSE
- Suppose we want to predict job performance of mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. (a) Determine the regression equation. (b) Determine the SSE.
|
Y |
X1 |
X2 |
|
1 |
40 |
25 |
|
2 |
45 |
20 |
|
1 |
38 |
30 |
|
3 |
50 |
30 |
|
2 |
48 |
28 |
|
3 |
55 |
30 |
|
3 |
53 |
34 |
|
4 |
55 |
36 |
|
4 |
58 |
32 |
|
3 |
40 |
34 |
|
5 |
55 |
38 |
|
3 |
48 |
28 |
|
3 |
45 |
30 |
|
2 |
55 |
36 |
|
4 |
60 |
34 |
|
5 |
60 |
38 |
|
5 |
60 |
42 |
|
5 |
65 |
38 |
|
4 |
50 |
34 |
|
3 |
58 |
38 |
Where Y is the Performance of the mechanics, X1 is the mechanical aptitude test and X2 is the personality test score that measure conscientiousness.
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