Answer to Question #217871 in Finance for Beauty Magadlela

Question

 data over the past six months.

Number of houses sold Monthly loan payments (in R1 000’s)

x y

160 3,7

250 5,6

800 7,5

450 11,3

120 18,9

50 28.4

The regression line equation is [1] y = 480,89x − 13,99. [2] y = −0,016x + 17,45. [3] y = 17,45x − 0,016. [4] y = −13,99x + 480,89. [5] none of the above

Answer 1

Solution:

Given:

Step 1: Find $X\cdot Y$  and $X^2$  as follows.

Step 2: Find the sum of every column:

$\sum X=1830, \sum Y=75.4, \sum X \cdot Y=16765, \sum X^{2}=947500$

Step 3: Use the following equations to find a and b :

$\begin{aligned} &a=\frac{\sum Y \cdot \sum X^{2}-\sum X \cdot \sum X Y}{n \cdot \sum X^{2}-\left(\sum X\right)^{2}}=\frac{75.4 \cdot 947500-1830 \cdot 16765}{6 \cdot 947500-1830^{2}} \approx 17.45 \\ &b=\frac{n \cdot \sum X Y-\sum X \cdot \sum Y}{n \cdot \sum X^{2}-\left(\sum X\right)^{2}}=\frac{6 \cdot 16765-1830 \cdot 75.4}{6 \cdot 947500-(1830)^{2}} \approx-0.01601 \end{aligned}$

Step 4: Substitute a and b in regression equation formula

$y=a+b \cdot x \\y=17.45-0.01601 \cdot x$

Thus, option [2] is correct.