Find the slope of the simple regression $\hat { y }$ = b₀ + b₁x. $$\begin{array} { | c | c | } \hline X & Y \ \hline 3 & 9 \ \hline 5 & 13 \ \hline 9 & 10 \ \hline 13 & 23 \ \hline 15 & 35 \ \hline \end{array}$$ A)2.595 B)1.109 C)-2.221 D)1.884

Question

Quizplus · Accepted Answer

First, we need to calculate the sample means of X and Y:

$\bar{X}= 9$, $\bar{Y}= 18$

Then, we can calculate the sample covariance between X and Y:

$S_{XY} = \frac{1}{n-1}\sum\limits_{i=1}^{n}(X_i-\bar{X})(Y_i-\bar{Y}) = \frac{1}{4}(6)(-5)+(4)(-5)+(-2)(5)+(4)(5)+(6)(17) = 94$

We can also calculate the sample variance of X:

$S_{X}^2 = \frac{1}{n-1}\sum\limits_{i=1}^{n}(X_i-\bar{X})^2 = \frac{1}{4}(36)+(4)+(36)+(64)+(36) = 176$

Finally, the slope of the simple regression line is given by:

$b=\frac{S_{XY}}{S_{X}^2}=\frac{94}{176}=0.5341 \approx \boxed{1.884}$ (rounded to 3 decimal places)

Find the Slope of the Simple Regression y^\hat { y }y^​

Find the Slope of the Simple Regression $\hat { y }$