Find the equation of the regression line for the given data. Then construct a sc

Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x=values, If meaningful The number of hours 6 students spent for a test and their scores on that test are shown below. (a) x = 2 hours (c)x = 13 hours (b) x = 4.5 hours (d) x = 3.5 hours Find the regression equation. y = x + (Round to three decimal places as needed.)

Explanation / Answer

Mean of X = X / n =    2.1232
Mean of Y = Y / n =   31.3214
(Xi - Mean)^2 =   45.9341
(Yi - Mean)^2 =   7268.71
(Xi-Mean)*(Yi-Mean) =   540.9965
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
Y = bo + b1 X  
  
Y'=6.3151+11.7777*X  

a.

when x=2hours then Y'=6.3151+11.7777*2

Y'=29.8705

b.

when x= 4.5hours then Y'=6.3151+11.7777*4.5

Y'=59.31475

c.

when x=13 hours then Y'=6.3151+11.7777*13

Y'=159.4252

d. when x=3.5 hours then Y'=6.3151+11.7777*3.5

Y'=47.53705

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 1 38 1.2616 44.6037 -7.5014 2 43 0.0152 136.3897 -1.4388 3 50 0.7688 348.8901 16.3774 4 49 3.5224 312.5329 33.1792 5 62 8.276 941.1765 88.2562 6 71 15.0296 1574.3913 153.826

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