Linear Regression Model

[gkv]

Hi

Can anyone assist me with the following question

The human resource manager of a large USA based IT company has derived a linear regression model to predict the current salary of an employee based on the employee's starting salary (in $), previous experience (in months) and years in education. The model's output is shown below:

Regression Statistics
R	0.8938​
R Square	0.5914​
Adjusted R Square	0.8685​
Standard Error	7,308.39550​
Sample Size	95​
	Coefficients	Standard Error	t Stat	p-level
Intercept	-2247.32​	4,165.04075​	-0.76211​	0.44808​
Starting Salary	26.17​	0.11447​	14.02690​	0.00000E+0​
Previous Experience	-15.37​	7.39860​	-1.03829​	0.08204​
Education	944.35​	349.76133​	2.15655​	0.13383​

By looking at the model's output what is an employee’s current salary if the employee started working with a salary of 20500$, has 2 years of previous experience and has been studying for 8 years? (Give your answer in 2 decimal points).

I have attempted this and come up with the following equations which I am sure are wrong

y = 26.17(20500) + [-2247.32 -15.37(24) + 944.35(8) ]
y = 26.17(20500) + [ -2247.32 + 26.17 - 15.37(24) + 944.35(8)]

 

[BigBeachBanana]

The linear regression model has the general form: [math]Y = \beta_0 + \sum_{i=1}^{n}\beta_ix_i + \epsilon[/math]where [imath]\beta_o[/imath] is the intercept, and [imath]\beta_i[/imath] are the coefficients of the regression model, aka explanatory variables.
I see where you get confused between "starting salary" and the intercept by your parenthesis. In this problem, the "starting salary" is an explanatory variable.
Can you identify the value of [imath]\beta_o, \beta_1, \beta_2,\beta_3[/imath] explicitly?

 

[gkv]

Hi

So if I am understanding you correctly the equation would be:
20500 = -2247.32-15.37(8)+26.17+944.35(8) + e
or
20500 = -2247.32-15.37(8)+26.17+944.35(8)

 

[BigBeachBanana]

Hi

So if I am understanding you correctly the equation would be:
20500 = -2247.32-15.37(8)+26.17+944.35(8) + e
or
20500 = -2247.32-15.37(8)+26.17+944.35(8)

The linear regression predicts current salary using starting salary, previous experience, and education.
So your Y is current salary, your [imath]\beta[/imath]s are the coefficients of starting salary, previous experience, and education.
Thus, the linear model is:
Current salary = -2247.32 + 26.17*(starting salary) -15.37*(previous experience) + 944.35*(education)
Now the question asks: By looking at the model's output, what is an employee's current salary if the employee started working with a salary of 20500$, has two years of previous experience, and has been studying for eight years?
Can you plug the corresponding values into the model?

 

[gkv]

The linear regression predicts current salary using starting salary, previous experience, and education.
So your Y is current salary, your [imath]\beta[/imath]s are the coefficients of starting salary, previous experience, and education.
Thus, the linear model is:
Current salary = -2247.32 + 26.17*(starting salary) -15.37*(previous experience) + 944.35*(education)
Now the question asks: By looking at the model's output, what is an employee's current salary if the employee started working with a salary of 20500$, has two years of previous experience, and has been studying for eight years?
Can you plug the corresponding values into the model?

Using that equation the corresponding values will be:
current salary = -2247.32 +26.17*(20500)-15.37*(24)+944.35*(8)
That gives an answer of $541K. that doesn't sound right?

 

[BigBeachBanana]

Using that equation the corresponding values will be:
current salary = -2247.32 +26.17*(20500)-15.37*(24)+944.35*(8)
That gives an answer of $541K. that doesn't sound right?

The question states two years of experience. Why are you using 24?

 

[gkv]

The human resource manager of a large USA based IT company has derived a linear regression model to predict the current salary of an employee based on the employee's starting salary (in $), previous experience (in months) and years in education. The model's output is shown below:

My assumption was to convert the 2 years into months

 

[BigBeachBanana]

The human resource manager of a large USA based IT company has derived a linear regression model to predict the current salary of an employee based on the employee's starting salary (in $), previous experience (in months) and years in education. The model's output is shown below:

My assumption was to convert the 2 years into months

You are correct. I've missed that part and it should be 24 months. The reason the answer is so high is because of the current salary coefficient. For every starting salary dollar, the model is predicting the current salary will be 26.17 times (i.e 20,500 * 26.17 = 536,485). Your previous answer stands correct 541K.