The table below gives the number of hours five randomly selected students spent
ID: 3319881 • Letter: T
Question
The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm test grades. Using this data, consider the equation of the regression line, y^=b0+b1x , for predicting the midterm test grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Step 5 of 6 : Find the error prediction when x=4 . Round your answer to three decimal places.
Hours Studying 0 2 4 5 6 Midterm Grades 76 86 87 91 99Explanation / Answer
calculation procedure for correlation
sum of (x) = x = 17
sum of (y) = y = 439
sum of (x^2)= x^2 = 81
sum of (y^2)= y^2 = 38823
sum of (x*y)= x*y = 1569
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 1569 - [ 5 * (17/5) * (439/5) ]/5- 1
= 15.28
and now to calculate r( x,y) = 15.28/ (SQRT(1/5*1569-(1/5*17)^2) ) * ( SQRT(1/5*1569-(1/5*439)^2)
=15.28 / (2.154*7.467)
=0.95
value of correlation is =0.95
REGRESSION
calculation procedure for regression
mean of X = X / n = 3.4
mean of Y = Y / n = 87.8
(Xi - Mean)^2 = 23.2
(Yi - Mean)^2 = 278.8
(Xi-Mean)*(Yi-Mean) = 76.4
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
= 76.4 / 23.2
= 3.2931
bo = Y / n - b1 * X / n
bo = 87.8 - 3.2931*3.4 = 76.60345
value of regression equation is, Y = bo + b1 X
Y'=76.60345+3.2931* X
& when x = 4, =>
Y'=76.60345+3.2931* 4 = 89.77585
( X) ( Y) X^2 Y^2 X*Y 0 76 0 5776 0 2 86 4 7396 172 4 87 16 7569 348 5 91 25 8281 455 6 99 36 9801 594Related Questions
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