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

Expert's answer

**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}\n\n&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 \\\\\n\n&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\n\n\\end{aligned}"

**Step 4**: Substitute a and b in regression equation formula

"y=a+b \\cdot x\n\n\\\\y=17.45-0.01601 \\cdot x"

Thus, option [2] is correct.

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