During Week 5, using your actual scores for Weeks 1, 2, 3, and 4 and your foreca

Question

During Week 5, using your actual scores for Weeks 1, 2, 3, and 4 and your forecast values, calculate a regression equation, r, and R2 for this data. What data did you use in your regression equation? The data is as follows: each discussion grade is worth a maximum of 15 points a piece, with two discussions being conducted each week. Each homework assignment is a maximum of 35 points each week. In all 4 weeks the maximum points were earned for the discussions and the following homework assignments grades were 34, 35, 33 and 30. 1. Which is the independent and dependent variable? 2. What is the regression equation, r, and R2 for your data? 3. Statistically, what does r and R2 tell you? 4. Based on your empirical evidence, how who well did you forecast your results? Justify your response. There are two different grades needed to be forecast here. One is discussion postings that have a maximum grade of 15 each, with two completed/graded each week. Full credit was received for each one (8 grades of 15) and the homework which was a maximum of 35 for each assignment, which were captured above. Can you adjust the equation to include both sets of grades to forecast? If you require additional data, please list what you need in your comment.

Explanation / Answer

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,

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

So, the prediction equation is: Y2 = 35.765 - 0.686X2

r = -1 x Multiple R = -0.837

R2 = 69.99%

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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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Forecast

Y1: For the coming week 5, Y1 = 15 and Y2 = 35.765 - 0.686 x 5 = 32.335

So, two discussion posts will earn 15, 15.

The assignment will earn 32.335

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

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