[tex]y = 0.51x + 0.0175[/tex]
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The line has the following format:
[tex]y = mx + b[/tex]
[tex]m = \frac{\sum (x-\overline{x})(y-\overline{y})}{\sum (x-\overline{x})^2}[/tex]
The means are:
[tex]\overline{x} = \frac{4 + 6 + 16 + 17}{4} = 10.75[/tex]
[tex]\overline{y} = \frac{2 + 3 + 8 + 9}{4} = 5.5[/tex]
The sums are:
[tex]\sum (x-\overline{x}) = (4 - 10.75) + (6 - 10.75) + (16 - 10.75) + (17 - 10.75)[/tex]
[tex]\sum (y-\overline{y}) = (2 - 5.5) + (3 - 5.5) + (8 - 5.5) + (9 - 5.5)[/tex]
With the help of a calculator, we find the slope:
[tex]\sum (x-\overline{x})(y-\overline{y}) = 68.5[/tex]
[tex]\sum (x-\overline{x})^2 = 134.75[/tex]
[tex]m = \frac{\sum (x-\overline{x})(y-\overline{y})}{\sum (x-\overline{x})^2} = \frac{68.5}{134.75} = 0.51[/tex]
Then
[tex]y = 0.51x + b[/tex]
Using the means, we find b.
[tex]5.5 = 0.51(10.75) + b[/tex]
[tex]b = 0.0175[/tex]
Thus
[tex]y = 0.51x + 0.0175[/tex]
With 13 commercials:
[tex]y = 0.51(13) + 0.0175 = 6.65[/tex]
The estimate is of 6.65 hundreds of cars sold.
A similar problem is given at https://brainly.com/question/16793283
