Question

Complete the following for the data set:

1. Scatter Plot
2. Calculate the regression line in Y-intercept form (do this piece by piece in Excel, or by hand)
3. Interpret in Words your Beta coefficient
4. If X=5; then your Y-hat equals what? Is this a good estimate or not (explain in words)
5. Plot the regression line
6. Use STATA to calculate and interpret the R2

Yi	Xi
2	11
4	9
4	14
6	9
8	9
10	8
10	13
11	5
13	6
17	5

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	89	85	86.9	192.5	-88.50
mean	8.90	8.50	SSxx	SSyy	SSxy

sample size ,   n =   10          
here, x̅ = Σx / n=   8.90   ,     ȳ = Σy/n =   8.50  
                  
SSxx =    Σ(x-x̅)² =    86.9000          
SSxy=   Σ(x-x̅)(y-ȳ) =   -88.5          
                  
estimated slope , ß1 = SSxy/SSxx =   -88.5   /   86.900   =   -1.02
                  
intercept,   ß0 = y̅-ß1* x̄ =   17.5639          
                  
so, regression line is   Ŷ =   17.564   +   -1.018   *x

when x is increased by 1 unit, y will be decreasd by 1.018

..............

Predicted Y at X=   5   is                  
Ŷ =   17.56387   +   -1.018412   *   5   =   12.47

R² = 0.4682

...............

THANKS

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