The table below gives the number of hours spent unsupervised each day as well as
ID: 3318328 • Letter: T
Question
The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, y^=b0+b1x , for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. 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 1 of 6 : Find the estimated slope. Round your answer to three decimal places.
Hours Unsupervised 0 0.5 1.5 2 3.5 4 5.5 Overall Grades 98 85 79 75 74 66 65Explanation / Answer
Line of Regression Y on X i.e Y = bo + b1 X
calculation procedure for regression
mean of X = X / n = 2.4286
mean of Y = Y / n = 77.4286
(Xi - Mean)^2 = 23.7143
(Yi - Mean)^2 = 785.71
(Xi-Mean)*(Yi-Mean) = -124.7857
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
= -124.7857 / 23.7143
= -5.26204
bo = Y / n - b1 * X / n
bo = 77.4286 - -5.26204*2.4286 = 90.208
value of regression equation is, Y = bo + b1 X
Y'=90.208-5.26204* X
slope = b1 = -5.262
X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 0 98 5.8981 423.1825 -49.9597 0.5 85 3.7195 57.3261 -14.6022 1.5 79 0.8623 2.4693 -1.4592 2 75 0.1837 5.8981 1.0409 3.5 74 1.1479 11.7553 -3.6734 4 66 2.4693 130.6129 -17.9589 5.5 65 9.4335 154.4701 -38.1732Related Questions
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