Question

A company determines an employee's starting salary according to the number of years of experience, as detailed in the table. Years of experience Salary 1 $52,150 2 $54,260 3 $56,285 4 $58,820 5 $60,126 Using technology, determine the line of fit, where x represents the number of years of experience and ŷ represents the salary. ŷ = 2535x + 50000 ŷ = −2535x + 50000 ŷ = 2076.1x + 50083 ŷ = −2076.1x + 50083

Answer 1

The correct line of fit for an employee's salary based on years of experience is ŷ = 2076.1x + 50083, since it provides a positive slope and closely matches the varying increments in salary. Therefore correct option is C

Step-by-step explanation:

The problem at hand is to determine the line of fit for the salary data of an employee based on their years of experience.

Given the data table that shows salaries increasing with experience, we are looking for a linear equation in the form of ŷ = mx + b, where x represents the years of experience and ŷ represents the salary.

The correct line of fit should show a positive slope, as salaries increase with experience.

Considering the salary increases with years of experience, we can eliminate the lines with a negative slope, which are ŷ = −2535x + 50000 and ŷ = −2076.1x + 50083 because they suggest that salaries decrease as experience increases, which is not the case according to the provided salary data.

The remaining options are ŷ = 2535x + 50000 and ŷ = 2076.1x + 50083.

Since the increases in salary do not match exactly $2535 each year, but vary, the precise regression line would likely have a non-rounded slope like 2076.1 and an adjusted y-intercept like 50083 to best fit the data points.

Therefore, the correct line of fit that represents the increase in salary with the increase in years of experience is likely ŷ = 2076.1x + 50083.