Consider a regression model Yi=β0+β1Xi+ui and suppose from a sample of 10 observations you are provided...

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

Solutions

Expert Solution

	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)

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

Please revert back in case of any doubt.

Please upvote. Thanks in advance.

orchestra answered 1 year ago

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