In: Statistics and Probability
This is a personal case study. Each case study will be unique to the student submitting it. • By Wednesday of Week 1 forecasts the scores you think you will achieve for Weeks, 1, 2, 3, and 4 and send them to your professor. • "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. • Prepare a case study document to answer the following questions. The case study should have a cover page, intro, and body that follows APA format. If a reference is used, such as our text, then a reference page should be included, and appropriate citation(s) should appear in the body of your case study. See the sample case study above for guidance. 1. 1. What data did you use in your regression equation? Which is the independent and dependent variable? 2. 2. What is the regression equation, r, and R2 for your data? 3. 3. Statistically, what does r and R2 tell you? 4. 4. Based on your empirical evidence, how who well did you forecast your results? Justify your response. You can use any method you like to complete this assignment; however, you need to show your work. Two items in Excel are useful. The correl function will return the correlation coefficient and add-in called "Data Analysis" has a function called regression that will provide all the rest of the information you should need. Below are the needed data: Actual scores Week1 4/15 0/15 28/35 40/40 Week2 8/15 8/15 35/35 Week3 10/15 12/15 30/35 70/70 Week4 10/15 8/15 20/35 Forecasted scores Week1 10/15 10/15 35/35 40/40 Week2 10/15 10/15 35/35 Week3 15/15 15/15 35/35 70/70 Week4 15/15 15/15 35/35 Need solutions please.
Week (x): 1 1 1 1 2 2 2 3 3 3 3 4 4 4
Actual Score (y): 4/15 0/15 28/35 40/40 8/15 8/15 35/35 10/15 12/15 30/35 70/70 10/15 8/15 20/35
1.1 Week (x) is independent variable and Actual score (y) is dependent variable.
2.2
3.3 r tells us the strength of linear relationship between x and y and r=0.1955 mans poor positive correlation between x and y.
R2 tells us proportion of total variation which is explained by linear regression and it is 0.03822 which shows linear regression explains 3.822% total variation of data and this is very low. Hence fitting is not good.
4.4. If we use independent variable as forecasted scores (X) then regression equation of y on X is
0.73224 +0.07104 X and R2 is 0.277 which is higher than previous R2 of regression equation of y on x. So it is better to use regression equation based on forcasting scores. Hence predicted value for week 5 is=1.087=100% (approximately).