Consider the data set shown below. Find the estimate of the slope of the least squares regression line. $$\begin{array} { c | c | c | c | c | c | c | c }
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$
A) 1.5
B) 0.94643
C) 1.49045
D) 0.9003

Question

Consider the data set shown below. Find the estimate of the slope of the least squares regression line. $$\begin{array} { c | c | c | c | c | c | c | c } 
\mathrm { y } & 0 & 3 & 2 & 3 & 8 & 10 & 11 \
\hline \mathrm { x } & - 2 & 0 & 2 & 4 & 6 & 8 & 10
\end{array}$$
A) 1.5
B) 0.94643
C) 1.49045
D) 0.9003

Quizplus · Accepted Answer

The slope of the least squares regression line is calculated as:$$b = \frac{\sum(x_i - \overline{x})(y_i - \overline{y})}{\sum(x_i - \overline{x})^2}$$where $x_i$ and $y_i$ are the data points, and $\overline{x}$ and $\overline{y}$ are the means of the $x$ and $y$ values, respectively.Plugging in the values from the data set, we get:$$b = \frac{(-2 - 4)(0 - 5.2857) + (0 - 4)(3 - 5.2857) + (2 - 4)(2 - 5.2857) + (4 - 4)(3 - 5.2857) + (6 - 4)(8 - 5.2857) + (8 - 4)(10 - 5.2857) + (10 - 4)(11 - 5.2857)}{(-2 - 4)^2 + (0 - 4)^2 + (2 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (8 - 4)^2 + (10 - 4)^2}$$$$b = \frac{-12.7143}{-42} = 0.94643$$Therefore, the estimate of the slope of the least squares regression line is 0.94643.

Consider the Data Set Shown Below A) 15 B) 0

Consider the Data Set Shown Below A) 15
B) 0