find the equation for the least squares regression line of the data described below.\n\na television sports…

find the equation for the least squares regression line of the data described below.\n\na television sports commentator recently declared that basketball teams that rely on the three-point shot cannot win championships. to see if the commentator had a valid point, a sports analyst reviewed game statistics from several teams over the past season.\n\nfor each of the teams, the analyst calculated what percentage of attempted field goals had been three-pointers, $x$, and the number of wins in the season, $y$.\n\n| percentage of shots taken from three-point range | number of wins in a season |\n| :---: | :---: |\n| 22 | 33 |\n| 22 | 26 |\n| 24 | 23 |\n| 29 | 55 |\n| 30 | 60 |\n\nround your answers to the nearest thousandth.\n$y = \\square x + \\square$

find the equation for the least squares regression line of the data described below.\n\na television sports commentator recently declared that basketball teams that rely on the three-point shot cannot win championships. to see if the commentator had a valid point, a sports analyst reviewed game statistics from several teams over the past season.\n\nfor each of the teams, the analyst calculated what percentage of attempted field goals had been three-pointers, $x$, and the number of wins in the season, $y$.\n\n| percentage of shots taken from three-point range | number of wins in a season |\n| :---: | :---: |\n| 22 | 33 |\n| 22 | 26 |\n| 24 | 23 |\n| 29 | 55 |\n| 30 | 60 |\n\nround your answers to the nearest thousandth.\n$y = \\square x + \\square$

Answer

Explanation:

Step1: List the data points and calculate sums

Let $x$ be the percentage and $y$ be the wins. $n = 5$ $\sum x = 22 + 22 + 24 + 29 + 30 = 127$ $\sum y = 33 + 26 + 23 + 55 + 60 = 197$ $\sum x^2 = 22^2 + 22^2 + 24^2 + 29^2 + 30^2 = 484 + 484 + 576 + 841 + 900 = 3285$ $\sum xy = (22 \cdot 33) + (22 \cdot 26) + (24 \cdot 23) + (29 \cdot 55) + (30 \cdot 60) = 726 + 572 + 552 + 1595 + 1800 = 5245$

Step2: Calculate the slope $b$

$$b = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{5(5245) - (127)(197)}{5(3285) - (127)^2} = \frac{26225 - 25019}{16425 - 16129} = \frac{1206}{296} \approx 4.074324$$

Step3: Calculate the y-intercept $a$

$$a = \frac{\sum y - b\sum x}{n}$$ $$a = \frac{197 - (4.074324)(127)}{5} = \frac{197 - 517.439148}{5} = \frac{-320.439148}{5} \approx -64.08783$$

Step4: Round to the nearest thousandth

$b \approx 4.074$ $a \approx -64.088$

Answer:

$y = 4.074x - 64.088$