Company | Cars (1,000s) |
Revenue ($ millions) |
---|---|---|
Company A | 11.5 | 118 |
Company B | 10.0 | 133 |
Company C | 9.0 | 98 |
Company D | 5.5 | 37 |
Company E | 4.2 | 40 |
Company F | 3.3 | 30 |
ANSWER:
(b) According to the scatter diagram developed in part (a), there appears to be a positive linear relationship between the number of cars in service and annual revenue. The points on a scatter diagram generally increase as the number of cars in service increases, indicating that there may be a correlation between the two variables.
(c) To develop an estimated regression equation using the least squares method, we need to calculate the slope and intercept of the regression line. Using formulas:
scss
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Slope = (NΣ(xy) - ΣxΣy) / (NΣ(x^2) - (Σx)^2)
Intercept = ȳ - Slope * x̄
Where N is the number of data points, x and y are the data points, x̄ and ȳ are the sample means of x and y, we get:
Makefile
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N = 6
Σx = 43.5
Σy = 456
Σxy = 5077
Σx^2 = 329.7
x̄ = 7.25
ȳ = 76
Slope = (6*5077 - 43.5*456) / (6*329.7 - 43.5^2) ≈ 12.886
Intercept = 76 - 12.886*7.25 ≈ -1.313
Therefore, the estimated regression equation is:
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ŷ = -1.313 + 12.886x
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