What I understood is that there are two components of grades – the discussion points and the assignments. We cannot anyway forecast both of them with one single equation. We need to have two separate regression equations for two separate dependent variables. The independent variable is going to be the ‘period number’
Y1: Discussion points;
So, this is the data,
Week Period (X1) Score (Y1)
1 1 15
1 2 15
2 3 15
2 4 15
3 5 15
3 6 15
4 7 15
4 8 15
SUMMARY OUTPUT
Regression Statistics
Multiple R 1
R Square 1
Adjusted R Square 1
Standard Error 0
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 0 0 #NUM! #NUM!
Residual 6 0 0
Total 7 0
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 15 0 65535 #NUM! 15 15 15 15
Period (X1) 0 0 65535 #NUM! 0 0 0 0
So, the prediction equation is Y1 = 15 + 0.X1 or, Y1 = 15
r = cannot be calculated here as all the scores are equal
R2 = 100%
Y2: Assignments
Week Period (X2) Score (Y2)
1 1 34
2 3 35
3 5 33
4 7 30.1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.836626596
R Square 0.699944061
Adjusted R Square 0.549916092
Standard Error 1.418273598
Observations 4
ANOVA
df SS MS F Significance F
Regression 1 9.3845 9.3845 4.665423813 0.163373404
Residual 2 4.023 2.0115
Total 3 13.4075
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 35.765 1.453297974 24.60954371 0.001647096 29.51196351 42.01803649 29.51196351 42.01803649
Period (X2) -0.685 0.317135618 -2.159959216 0.163373404 -2.049524431 0.679524431 -2.049524431 0.679524431
So, the prediction equation is: Y2 = 35.765 – 0.686X2
r = -1 x Multiple R = -0.837
R2 = 69.99%
————————————–
r is the correlation coefficient. If r is positive than the two variables are positively correlated, and for r being negative, they are negatively correlated. The value of r can come between 0 and +/-1 with higher being the absolute value, higher the degree of correlation. In the first, case i.e. for Y1, the values cannot be calculated as all the Y1 values are equal. For Y2, the negative correlation is strong with r being equal to -0.837
R2 stands form how much the raw data explains the regression model derived. For example, 69.99% of the given data explains the model Y2 = 35.765 – 0.686X2. The R2 value should be more than 70% at least for a reliable estimate of regression. Both the models of Y1 and Y2 are good as for both, the R2 values are >= 70%.
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