Question

Consider a regression model Y_i=β₀₊β₁X_i+u_i and suppose from a sample of 10 observations you are provided the following information:

∑10i=1Yi=71;  ∑10i=1Xi=42;  ∑10i=1XiYi=308; ∑10i=1X2i=196

Given this information, what is the predicted value of Y, i.e.,Yˆ for x = 12?

1. 14

2. 11

3. 13

4. 12

5. 15

Answer 1

	X	Y	XY	X²
total sum	42.000	71.000	308.00	196.000
mean	4.2000	7.1000

SSxx =    Σx² - (Σx)²/n =   19.600
SSxy=   Σxy - (Σx*Σy)/n =   9.800

estimated slope , ß1 = SSxy/SSxx =   9.800   /   19.600   =   0.5000
                  
intercept,   ß0 = y̅-ß1* x̄ =   5.0000          
                  
so, regression line is   Ŷ =   5.00   +   0.50   *x

Predicted Y at X=   12   is                  
Ŷ =   5.000   +   0.500   *   12   =   11.000
option (2)

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Please revert back in case of any doubt.

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