The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: (a) Find the equation of the linear regression model and draw the regression line. (b) Estimate the final examination grade of a student who received a grade of 85 on the midterm report. X: 77 50 71 72 81 94 96 99 67 Y: 82 66 78 34 74 85 99 99 68
Added by Cindy H.
Step 1
Mean of X (x̄) = (77+50+71+72+81+94+96+99+67) / 9 = 784 / 9 = 87 Mean of Y (ȳ) = (82+66+78+34+74+85+99+99+68) / 9 = 685 / 9 = 76.11 Show more…
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The grades of a class of 9 students on a midterm report $(x)$ and on the final examination $(y)$ are as follows: $$ \begin{array}{c|ccccccccc} x & 77 & 50 & 71 & 72 & 81 & 94 & 96 & 99 & 67 \\ \hline y & 82 & 66 & 78 & 34 & 47 & 85 & 99 & 99 & 68 \end{array} $$ (a) Estimate the linear regression line. (b) Estimate the final examination grade of a student who received a grade of 85 on the midterm report.
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The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are shown below. Use the data to complete parts (a) and (b). x | 77 50 73 71 83 90 95 99 68 y | 81 67 79 36 49 80 99 99 70 (a) Estimate the linear regression line. ŷ = _ + (_)x (Round the constant to one decimal place as needed. Round the coefficient to three decimal places as needed.) (b) Estimate the final examination grade of a student who received a grade of 87 on the midterm report. ŷ = _ (Round to one decimal place as needed.)
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Find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of $y$ for each of the $x$ -values, if meaningful. If the $x$ -value is not meaningful to predict the value of $y,$ explain why not. If convenient, use technology. Hours Studying and Test Scores The number of hours 9 students spent studying for a test and their scores on that test $$\begin{array}{|l|c|c|c|c|c|c|c|c|c|} \hline \text { Hours spent studying, } \boldsymbol{x} & 0 & 2 & 4 & 5 & 5 & 5 & 6 & 7 & 8 \\ \hline \text { Test scores, } \boldsymbol{y} & 40 & 51 & 64 & 69 & 73 & 75 & 93 & 90 & 95 \\ \hline \end{array}$$ (a) $x=3$ hours (b) $x=6.5$ hours (c) $x=13$ hours (d) $x=4.5$ hours
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