Question

Home work thanks need help with this problem multi part question

Answer 1

$a)\text{ }ŷ=2273.46939X+49324.4898$

b) $2273.47

c) The expected salary with 13 years of experience is $78879.59

Explanation:

a) To write a linear model, we will use the linear equation formula:

y = mx + b

m = slope, b = y-intercept

First we need to find the slope using the formula:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

Picking any two points on the table, we use in the formula:

$\begin{gathered} (0,\text{ 49900) and (2, 52400)} \\ x_1=0,y_1=49900,x_2=2,y_2\text{ = }52400 \\ \text{slope = }\frac{52400\text{ - 49900}}{2-0} \\ \text{slope = 2500/2} \\ \text{slope = 12}50 \\ \end{gathered}$

There is something wrong with the values in the table. The slope is supposed to be constant for any two points in the table but that is not so here.

I will be using a linear regression instead:

$\begin{gathered} Regression\text{ }Equation\colonŷ=bX+a \\ X\text{ = years of experience} \\ ŷ\text{ = salary in dollars} \end{gathered}$

Graphing the values, we have:

$ŷ=2273.46939X+49324.4898$

b) The slope of the model we got is 2273.47

It means the rate of salary per year of experience is $2273.47

c) for 13 years of experience, x = 13

$\begin{gathered} we\text{ replace X with 13:} \\ ŷ=2273.46939(13)+49324.4898 \\ ŷ\text{ = 78879.59} \end{gathered}$

The expected salary with 13 years of experience is $78879.59