Problem 3: A researcher is interested in determining whether there is a relationship between grades and hours studied for statistics. Hours studied(X) Grade on final(Y) 1 20 2 30 4 40 7 60 6 70 7 78 8 83 9 98 1- You are given data for Xi (independent variable) and Yi (dependent variable). 2- Calculate the correlation coefficient, r: r = -1 ≤ r ≤ 1 3- Calculate the coefficient of determination: r2 = = 0 ≤ r2 ≤ 1 This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi) 4- Calculate the regression coefficient b1 (the slope): b1 = = Note that you have already calculated the numerator and the denominator for parts of r. Other than a single division operation, no new calculations are required. 5- Calculate the regression coefficient b0 (the Y-intercept, or constant): b0 = = 6- The regression equation (a straight line) is: = b0 + b1Xi Excel regression analysis Conclusion:
Topic: Regression
Problem 3: A researcher is interested in determining whether there is a relationship between grades and hours studied for statistics.
|
Hours studied(X) |
Grade on final(Y) |
|
1 |
20 |
|
2 |
30 |
|
4 |
40 |
|
7 |
60 |
|
6 |
70 |
|
7 |
78 |
|
8 |
83 |
|
9 |
98 |
1- You are given data for Xi (independent variable) and Yi (dependent variable).
2- Calculate the correlation coefficient, r:
r = -1 ≤ r ≤ 1
3- Calculate the coefficient of determination: r2 = =
0 ≤ r2 ≤ 1
This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi)
4- Calculate the regression coefficient b1 (the slope):
b1 = =
Note that you have already calculated the numerator and the denominator for parts of r. Other than a single division operation, no new calculations are required.
5- Calculate the regression coefficient b0 (the Y-intercept, or constant):
b0 = =
6- The regression equation (a straight line) is:
= b0 + b1Xi
- Excel regression analysis
Conclusion:
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