use linear regression to find the equation for the linear function that best fits this data. round to two…

use linear regression to find the equation for the linear function that best fits this data. round to two decimal places.\n y = \n basic funcs trig \n x \n hint \n s \n ( ) | | π ∞ dne \n ← → \n x 1 2 3 4 5 6 \n y 862 1093 1264 1587 1953 2550

use linear regression to find the equation for the linear function that best fits this data. round to two decimal places.\n y = \n basic funcs trig \n x \n hint \n s \n ( ) | | π ∞ dne \n ← → \n x 1 2 3 4 5 6 \n y 862 1093 1264 1587 1953 2550

Answer

Explanation:

Step1: Calculate sums

Let (n = 6). Calculate (\sum_{i = 1}^{n}x_{i}=1 + 2+3 + 4+5 + 6=21), (\sum_{i = 1}^{n}y_{i}=862+1093 + 1264+1587+1953+2550 = 9319), (\sum_{i = 1}^{n}x_{i}^{2}=1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}=1 + 4+9+16+25+36 = 91), (\sum_{i = 1}^{n}x_{i}y_{i}=1\times862+2\times1093+3\times1264+4\times1587+5\times1953+6\times2550=862 + 2186+3792+6348+9765+15300=38253).

Step2: Calculate slope (m)

The formula for the slope (m) of the regression - line is (m=\frac{n\sum_{i = 1}^{n}x_{i}y_{i}-\sum_{i = 1}^{n}x_{i}\sum_{i = 1}^{n}y_{i}}{n\sum_{i = 1}^{n}x_{i}^{2}-(\sum_{i = 1}^{n}x_{i})^{2}}). Substitute the values: (m=\frac{6\times38253-21\times9319}{6\times91 - 21^{2}}=\frac{229518-195699}{546 - 441}=\frac{33819}{105}\approx322.09).

Step3: Calculate intercept (b)

The formula for the intercept (b) is (b=\frac{\sum_{i = 1}^{n}y_{i}-m\sum_{i = 1}^{n}x_{i}}{n}). (b=\frac{9319-322.09\times21}{6}=\frac{9319 - 6763.89}{6}=\frac{2555.11}{6}\approx425.85).

Answer:

(y = 322.09x+425.85)