Find the equation for the least squares regression line of the data described below.Doug is a math teacher at a large school. He wonders if his test problems are too wordy. Doug is curious whether the wordiness is affecting student performance.For the last several tests, Doug computes the average number of words in each question, x, as well as the average percentage scores on the tests, y.\begin{tabular}{|c|c|}\hline Average question length & Average student score \\\hline 10.87 & 81.55 \\\hline 15.74 & 72.28 \\\hline 17.05 & 79.56 \\\hline 26.97 & 67.27 \\\hline 31.47 & 68.92 \\\hline 37.19 & 78.85 \\\hline 45.90 & 52.99 \\\hline 46.14 & 65.48 \\\hline\end{tabular}Round your answers to the nearest thousandth.y=□x+
Q. Find the equation for the least squares regression line of the data described below.Doug is a math teacher at a large school. He wonders if his test problems are too wordy. Doug is curious whether the wordiness is affecting student performance.For the last several tests, Doug computes the average number of words in each question, x, as well as the average percentage scores on the tests, y.\begin{tabular}{|c|c|}\hline Average question length & Average student score \\\hline 10.87 & 81.55 \\\hline 15.74 & 72.28 \\\hline 17.05 & 79.56 \\\hline 26.97 & 67.27 \\\hline 31.47 & 68.92 \\\hline 37.19 & 78.85 \\\hline 45.90 & 52.99 \\\hline 46.14 & 65.48 \\\hline\end{tabular}Round your answers to the nearest thousandth.y=□x+
Calculate mean x values: Calculate the mean of the x values (average question length). (10.87+15.74+17.05+26.97+31.47+37.19+45.90+46.14)/8=231.33/8=28.91625.
Calculate mean y values: Calculate the mean of the y values (average student score). (81.55+72.28+79.56+67.27+68.92+78.85+52.99+65.48)/8=566.9/8=70.8625.
Calculate numerator of slope: Calculate the numerator of the slope b1 of the regression line.Summation of (xi−mean of x)∗(yi−mean of y) for all data points.= (10.87−28.91625)∗(81.55−70.8625)+(15.74−28.91625)∗(72.28−70.8625)+…+(46.14−28.91625)∗(65.48−70.8625).= (−18.04625∗10.6875)+(−13.17625∗1.4175)+…+(17.22375∗−5.3825).= −192.90703125−18.67640625+…−92.67640625.