Question #217871

 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


1
Expert's answer
2021-07-23T11:21:01-0400

Solution:

Given:


Step 1: Find XYX\cdot Y  and X2X^2  as follows.


Step 2: Find the sum of every column:

X=1830,Y=75.4,XY=16765,X2=947500\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 :

a=YX2XXYnX2(X)2=75.494750018301676569475001830217.45b=nXYXYnX2(X)2=616765183075.46947500(1830)20.01601\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+bxy=17.450.01601xy=a+b \cdot x \\y=17.45-0.01601 \cdot x

Thus, option [2] is correct.


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