Consider a regression modelY i 0 1 X i u i and suppose from a sa...

X Y XY X total sum 42000 71000 30800 196000 mean 42000 71000 SSxx x xn ....

Consider a regression model Yi=Î²0+Î²1Xi+ui and suppose from a sample of 10 observations you are provided the following...

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Consider a regression modelY_i=Î²₀₊Î²₁X_i₊u_iand suppose from a sample of 10 observations you are provided thefollowing information:
âˆ‘10i=1Yi=71;Â Â âˆ‘10i=1Xi=42;Â Â âˆ‘10i=1XiYi=308;âˆ‘10i=1X2i=196
Given this information, what is the predicted value ofY, i.e.,YË† for x = 12?
1. 14
2. 11
3. 13
4. 12
5. 15

Answer & Explanation Solved by verified expert

3.9 Ratings (516 Votes)

	X	Y	XY	XÂ²
total sum	42.000	71.000	308.00	196.000
mean	4.2000	7.1000

SSxx = Â Â Î£xÂ² - (Î£x)Â²/n =Â Â 19.600
SSxy=Â Â Î£xy - (Î£x*Î£y)/n =Â Â 9.800

estimated slope , ÃŸ1 = SSxy/SSxx =Â Â 9.800Â Â /Â Â 19.600Â Â =Â Â 0.5000
Â Â Â Â Â Â Â Â Â Â Â Â Â Â
intercept,Â Â ÃŸ0 = yÌ…-ÃŸ1* xÌ„ =Â Â 5.0000Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â Â
so, regression line isÂ Â YÌ‚ =Â Â 5.00Â Â +Â Â 0.50Â Â *x

Predicted Y at X=Â Â 12Â Â isÂ Â Â Â Â Â Â Â Â Â Â Â Â Â
YÌ‚ =Â Â 5.000Â Â +Â Â 0.500Â Â *Â Â 12Â Â =Â Â 11.000
option (2)

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

Please revert back in case of any doubt.

Please upvote. Thanks in advance.

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