Question

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.

Week 1-4

Actual score Forecast score

25 25

22 25

35 35

35 35

1. What data did you use in your regression equation? 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.

Answer 1

1)

We have used actual score and forecast score in regression equation.

Indepednent = actual score

Dependent = forecast score

2)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	117	120	136.75	100.0	115.00
mean	29.25	30.00	SSxx	SSyy	SSxy

sample size ,   n =   4          
here, x̅ = Σx / n=   29.25   ,     ȳ = Σy/n =   30.00  
                  
SSxx =    Σ(x-x̅)² =    136.7500          
SSxy=   Σ(x-x̅)(y-ȳ) =   115.0          
                  
estimated slope , ß1 = SSxy/SSxx =   115.0   /   136.750   =   0.84
                  
intercept,   ß0 = y̅-ß1* x̄ =   5.40          
                  
so, regression line is   Ŷ =   5.40   +   0.84   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    3.291          
                  
std error ,Se =    √(SSE/(n-2)) =    1.283          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.98          
                  
R² =    (Sxy)²/(Sx.Sy) =    0.9671

3)

R tells how strong and direction of the relationship

R sqaure tell how much variation in y can be explained by x

4)

Results are very well forecast results as we can the residuals are almost nthing.

THANKS

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