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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.




Average question length
Average student score


10.87
81.55


15.74
72.28


17.05
79.56


26.97
67.27


31.47
68.92


37.19
78.85


45.90
52.99


46.14
65.48




Round your answers to the nearest thousandth.

y=◻x+

Find the equation for the least squares regression line of the data described below.\newlineDoug 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.\newlineFor the last several tests, Doug computes the average number of words in each question, x x , as well as the average percentage scores on the tests, y y .\newline\begin{tabular}{|c|c|}\newline\hline Average question length & Average student score \\\newline\hline 1010.8787 & 8181.5555 \\\newline\hline 1515.7474 & 7272.2828 \\\newline\hline 1717.0505 & 7979.5656 \\\newline\hline 2626.9797 & 6767.2727 \\\newline\hline 3131.4747 & 6868.9292 \\\newline\hline 3737.1919 & 7878.8585 \\\newline\hline 4545.9090 & 5252.9999 \\\newline\hline 4646.1414 & 6565.4848 \\\newline\hline\newline\end{tabular}\newlineRound your answers to the nearest thousandth.\newliney=x+ y=\square x+

Full solution

Q. Find the equation for the least squares regression line of the data described below.\newlineDoug 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.\newlineFor the last several tests, Doug computes the average number of words in each question, x x , as well as the average percentage scores on the tests, y y .\newline\begin{tabular}{|c|c|}\newline\hline Average question length & Average student score \\\newline\hline 1010.8787 & 8181.5555 \\\newline\hline 1515.7474 & 7272.2828 \\\newline\hline 1717.0505 & 7979.5656 \\\newline\hline 2626.9797 & 6767.2727 \\\newline\hline 3131.4747 & 6868.9292 \\\newline\hline 3737.1919 & 7878.8585 \\\newline\hline 4545.9090 & 5252.9999 \\\newline\hline 4646.1414 & 6565.4848 \\\newline\hline\newline\end{tabular}\newlineRound your answers to the nearest thousandth.\newliney=x+ y=\square x+
  1. 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(10.87 + 15.74 + 17.05 + 26.97 + 31.47 + 37.19 + 45.90 + 46.14) / 8 = 231.33 / 8 = 28.91625.
  2. 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(81.55 + 72.28 + 79.56 + 67.27 + 68.92 + 78.85 + 52.99 + 65.48) / 8 = 566.9 / 8 = 70.8625.
  3. Calculate numerator of slope: Calculate the numerator of the slope b1b_1 of the regression line.\newlineSummation of (ximean of x)(yimean of y)(x_i - \text{mean of } x) * (y_i - \text{mean of } y) for all data points.\newline= (10.8728.91625)(81.5570.8625)+(15.7428.91625)(72.2870.8625)++(46.1428.91625)(65.4870.8625)(10.87 - 28.91625) * (81.55 - 70.8625) + (15.74 - 28.91625) * (72.28 - 70.8625) + \ldots + (46.14 - 28.91625) * (65.48 - 70.8625).\newline= (18.0462510.6875)+(13.176251.4175)++(17.223755.3825)(-18.04625 * 10.6875) + (-13.17625 * 1.4175) + \ldots + (17.22375 * -5.3825).\newline= 192.9070312518.67640625+92.67640625-192.90703125 - 18.67640625 + \ldots - 92.67640625.

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