Question

The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
y
xy
100
600
10,000
60,000
144
850
20,736
122,400
225
1,300
50,625
292,500
324
1,900
104,976
615,600
400
2,300
160,000
920,000
Σχ=1,193 | Σy=6,950 | Ex?=346,337 | Σxy=2,010,500
Which regression equation correctly models the data?
X
xy=5.83x-1.04
y = 5.83x + 17
y = 5.71x + 29
y
= 5.71x + 27.6
Submitted

Answer 1

The regression equation of the table is y = 5.71x + 27.6

How to estimate the regression equation?

From the table of values, we have the following parameters:

$\sum x = 1193$

$\sum y = 6950$

$\sum x^2 = 346337$

$\sum xy = 2010500$

Calculate A using

$A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}$

This gives

$A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}$

Evaluate

$A = \frac{8515650}{308436}$

Divide

A = 27.6

Calculate B using

$B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}$

This gives

$B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}$

Evaluate

$B = \frac{1761150}{308436}$

Divide

B = 5.71

The regression equation is represented as:

y = Bx + A

So, we have

y = 5.71x + 27.6

Hence, the regression equation of the table is y = 5.71x + 27.6

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