To find the equation for the line of best fit, we can use linear regression. The equation of the line of best fit is given by y = mx + b, where y is the dependent variable (salary), x is the independent variable (years of experience), m is the slope of the line, and b is the y-intercept.
Using the formula for m (slope) and b (y-intercept) in linear regression:
m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
b = (Σy - mΣx) / n
Where n is the number of data points, Σxy is the sum of the products of the x and y values, Σx is the sum of the x values, Σy is the sum of the y values, and Σx^2 is the sum of the squares of the x values.
In this case, we have the following data:
x: 0, 1, 2, 3, 4, 5
y: 40000, 42150, 44260, 46785, 48820, 51126
First, calculate the sums:
Σx = 0 + 1 + 2 + 3 + 4 + 5 = 15
Σy = 40000 + 42150 + 44260 + 46785 + 48820 + 51126 = 273141
Σxy = (0 * 40000) + (1 * 42150) + (2 * 44260) + (3 * 46785) + (4 * 48820) + (5 * 51126) = 1323655
Σx^2 = (0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55
Using the formulas for m and b, we can calculate:
m = (6 * 1323655 - 15 * 273141) / (6 * 55 - 15^2) = 65515 / 45 ≈ 1455.89
b = (273141 - 1455.89 * 15) / 6 = 1316.84
So the equation for the line of best fit is y = 1455.89x + 1316.84
Plugging in x = 7:
y = 1455.89(7) + 1316.84
y ≈ 10205.23 + 1316.84
y ≈ 11522.07
Rounding to the nearest dollar, the predicted salary for an employee with 7 years of experience is approximately $11,522. Therefore, the correct answer is not among the provided options.
A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Years of experience: 0, 1, 2, 3, 4, 5 Salary: $40000, $42150, $44260, $46785, $48820, $51126
Use the equation for the line of best fit to predict the salary for an employee with 7 years of experience? (Round your answer to the nearest dollar.)
a.$52,900
b.$53,340
c.$53,914
d.$55,573
use one of the provided answers
1 answer
1 answer