A researcher is interested in determining whether there is a relationship between grades and hours studied for statistic
Posted: Mon Jul 11, 2022 11:56 am
A researcher is interested in determining whether there is arelationship between grades and hours studied for statistics.
Hours studied(X)
Grade on final(Y)
1
20
2
25
4
40
7
59
6
62
7
72
8
83
9
98
1- You are given data for Xi (independentvariable) and Yi (dependentvariable).
2- Calculate the correlation coefficient, r:
r= -1≤ r ≤ 1
3- Calculate the coefficient ofdetermination: r2 = =
0 ≤ r2 ≤ 1
This is the proportion of the variation in the dependentvariable (Yi) explained by the independent variable(Xi)
4- Calculate the regressioncoefficient b1 (theslope):
b1 = =
Note that you have already calculated the numerator and thedenominator for parts of r. Other than a single divisionoperation, no new calculations are required.
5- Calculate the regression coefficient b0 (theY-intercept, or constant):
b0 = =
6- The regression equation (a straight line) is:
=b0 +b1Xi
B. Excel regression analysis
Conclusion:
Hours studied(X)
Grade on final(Y)
1
20
2
25
4
40
7
59
6
62
7
72
8
83
9
98
1- You are given data for Xi (independentvariable) and Yi (dependentvariable).
2- Calculate the correlation coefficient, r:
r= -1≤ r ≤ 1
3- Calculate the coefficient ofdetermination: r2 = =
0 ≤ r2 ≤ 1
This is the proportion of the variation in the dependentvariable (Yi) explained by the independent variable(Xi)
4- Calculate the regressioncoefficient b1 (theslope):
b1 = =
Note that you have already calculated the numerator and thedenominator for parts of r. Other than a single divisionoperation, no new calculations are required.
5- Calculate the regression coefficient b0 (theY-intercept, or constant):
b0 = =
6- The regression equation (a straight line) is:
=b0 +b1Xi
B. Excel regression analysis
Conclusion: