Question

A researcher surveyed 12 men who lost their fathers earlier in their lives.  His survey included the age of the subjects when their fathers died and their confidence that they would someday be happily married themselves (100 point scale – higher score = more confidence).  The results are shown below.

Mx=15 My =60

SSx=348 SSy=5198

SPxy=933

Age	Confidence Rating
12	34
8	30
11	89
21	69
15	55
7	38
18	78
23	66
22	89
19	79
9	35
15	58

Write a short interpretation of the effect size.

Write the equation for the regression line.

State, in words, the meaning of the regression equation.

Can you estimate a confidence rating for a man who lost his father at 30 years old? Why or why not?

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	180.00	720.00	348.00	5198.00	933.00
mean	15.00	60.00	SSxx	SSyy	SSxy

sample size ,   n =   12          
here, x̅ = Σx / n=   15.000   ,     ȳ = Σy/n =   60.000  
                  
SSxx =    Σ(x-x̅)² =    348.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   933.0          
                  
R² =    (Sxy)²/(Sx.Sy) =    0.4812

effect size = 0.4812

approx 0.4812 proportion of observation of variable confidence rating is explained by variable age

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estimated slope , ß1 = SSxy/SSxx =   933.0   /   348.000   =   2.68103
                  
intercept,   ß0 = y̅-ß1* x̄ =   19.78448          
                  
so, regression line is   Ŷ =   19.784   +   2.681   *x
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for every 1 year increase in age, confidence rating is predicted to be increase by 2.681

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Predicted Y at X=   30   is                  
Ŷ =   19.7845   +   2.6810   *   30   =   100.22