Compute the least-squares regression line for the given data set. $\begin{array}{c|cccccc}
x & 2 & 3 & 4 & 5 & 6 & 7 \
\hline y & 17.1 & 18.6 & 22.7 & 23.4 & 25.3 & 29
\end{array}$

A) $y = 2.2943 x + 12.3590$
B) $y = 2.3800 x + 12.3590$
C) $y = 12.3590 x + 2.2943$
D) $y = 2.3800 x + 17.1$

Question

Compute the least-squares regression line for the given data set. $\begin{array}{c|cccccc}
x & 2 & 3 & 4 & 5 & 6 & 7 \
\hline y & 17.1 & 18.6 & 22.7 & 23.4 & 25.3 & 29
\end{array}$

A) $y = 2.2943 x + 12.3590$
B) $y = 2.3800 x + 12.3590$
C) $y = 12.3590 x + 2.2943$
D) $y = 2.3800 x + 17.1$

Quizplus · Accepted Answer

To find the least-squares regression line, we first calculate the means of $x$ and $y$, the slope ($m$), and the y-intercept ($b$) using the formulas:$$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$$$b = \bar{y} - m\bar{x}$$where $n$ is the number of data points.Given data:$x = [2, 3, 4, 5, 6, 7]$$y = [17.1, 18.6, 22.7, 23.4, 25.3, 29]$Calculations:$\sum x = 27$, $\sum y = 136.1$, $\sum xy = 736.1$, $\sum x^2 = 147$, $n = 6$Mean of $x$, $\bar{x} = \frac{27}{6} = 4.5$Mean of $y$, $\bar{y} = \frac{136.1}{6} = 22.6833$Slope ($m$):$$m = \frac{6(736.1) - (27)(136.1)}{6(147) - (27)^2} = \frac{4416.6 - 3674.7}{882 - 729} = \frac{741.9}{153} = 2.2943$$Y-intercept ($b$):$$b = 22.6833 - 2.2943(4.5) = 22.6833 - 10.32435 = 12.35895$$Thus, the least-squares regression line is $y = 2.2943x + 12.3590$.

Compute the Least-Squares Regression Line for the Given Data Set x234567y17.118.622.723.425.329\begin{array}{c|cccccc}x & 2 & 3 & 4 & 5 & 6 & 7 \\\hline y & 17.1 & 18.6 & 22.7 & 23.4 & 25.3 & 29\end{array}xy​217.1​318.6​422.7​523.4​625.3​729​​

Compute the Least-Squares Regression Line for the Given Data Set $\begin{array}{c|cccccc}x & 2 & 3 & 4 & 5 & 6 & 7 \\\hline y & 17.1 & 18.6 & 22.7 & 23.4 & 25.3 & 29\end{array}$