1. The following table shows the midterm and linal exam grades obtained for students in a database course. \[ (4+5+6) \] \begin{tabular}{|l|l|} \hline Midterm Fxam \( (x) \) & Final Exam \( (y) \) \\ \hline 2 & 84 \\ \hline 50 & 63 \\ \hline 82 & 77 \\ \hline 74 & 78 \\ \hline 94 & 90 \\ \hline 86 & 75 \\ \hline 59 & 49 \\ \hline 83 & 79 \\ \hline 65 & 77 \\ \hline 33 & 52 \\ \hline \end{tabular} i. Do \( x \) and \( y \) seem to have a linear relationship? Explain. ii. Use the method of least squares to find an equation for the prediction of a student's final exam grade based on the student's midterm grade in the course. iii. Predict the final exam grade of a student who received a 94 on the midterm exam.
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To determine if x and y have a linear relationship, we can plot the data points on a graph and see if they roughly form a straight line. Alternatively, we can calculate the correlation coefficient, which measures the strength and direction of a linear relationship 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 as follows: $$ \begin{array}{c|ccccccccc} \mathbf{X} & 77 & 50 & 71 & 72 & 81 & 94 & 96 & 99 & 67 \\ \hline \boldsymbol{y} & 82 & 66 & 78 & 34 & 47 & 85 & 99 & 99 & 68 \end{array} $$ (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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