Linear regression

freeze4real

Hi guys,

I need some help with linear regression, especially interpreting it on excel.

I don't need the full depth of it as I'm doing just the basics in econometrics but if anyone is willingly to help me with it I'll be grateful.

I have attached a linear regression picture, and the question is how does your family income affects sibling wages, or is there any relationship between family income and children wages ?

andrew

Which exact bits are you having trouble interpreting? Which bit of that excel result do you understand?

freeze4real

andrew wrote: »

Which exact bits are you having trouble interpreting? Which bit of that excel result do you understand?

Hi,

Thanks for the reply I want to find out if the parents income affects the child's income, to do so were do I start from.

From what I can ell in class, I should start from the slope and intercept, ability and Family inc.

andrew

Just so I'm completely clear about what I'm looking at here (cos it's been a little while since I did this), what data did you have? As in, did you have the child's in come in euro/dollars etc, the family income in euro/dollars, etc, and then a measure of ability?

andrew

To simplify your output there, what that excel spreadsheet translates to is an equation which says:

(child's income) = 7.84 + 0.3*(ability) + 0.28*(family income)

This makes it slightly easier to interpret. I don't wanna give you the answer so Now what you need to think about is:

• What does the number before 'ability' and 'family income' actually mean? What does the intercept mean?
• Which number (coefficient) is the one you care about
• Does it have the sign you'd expect it to have (positive or negative) given the theory you're working from?
• And most importantly, is it stastically significant? For this, you look at the t-value or p-value associate with the coefficient; is sufficient for your confidence level?

freeze4real

andrew wrote: »

To simplify your output there, what that excel spreadsheet translates to is an equation which says:

(child's income) = 7.84 + 0.3*(ability) + 0.28*(family income)

This makes it slightly easier to interpret. I don't wanna give you the answer so Now what you need to think about is:

• What does the number before 'ability' and 'family income' actually mean? What does the intercept mean?
• Which number (coefficient) is the one you care about
• Does it have the sign you'd expect it to have (positive or negative) given the theory you're working from?
• And most importantly, is it stastically significant? For this, you look at the t-value or p-value associate with the coefficient; is sufficient for your confidence level?

Hi again sorry for late reply.

I don't understand this but I will guess.

The number before ability is the slope and the one after family income is the intercept. They 're both positive.

I'm trying to interpret this, If your ability goes up by .301 your family income goes up by 0.27 as your income depends on the ability of doing the job.

Am I far off ?

noodler

I am just going to stick this in here in case it is any use to you.

http://www.ats.ucla.edu/stat/stata/output/reg_output.htm

andrew

freeze4real wrote: »

Hi again sorry for late reply.

I don't understand this but I will guess.

The number before ability is the slope and the one after family income is the intercept. They 're both positive.

I'm trying to interpret this, If your ability goes up by .301 your family income goes up by 0.27 as your income depends on the ability of doing the job.

Am I far off ?

The first number, without any coefficient, is the intercept. It tells you how much a person would earn, if the other two coefficients were 0 (according to the data you have).

Whatever book you're using should a have a specific bit on interpreting the numbers in front of the coefficients, but to offer some explanation:

Remember, the point of a regression is to try to figure out what factors affect some other factor of interest. The factor you're interested in is called the dependant variable, and the other factors which you think might affect the dependant variable are the independent variables.

In your case, child's income is the dependant variable, and family income and ability are the independent variables. I figure you probably already have an idea of this already, all you need to do now is relate this to the equation above.

Imagine, then, the output of that equation when you change (ability) by a single unit; you said that that affects (family income). But how? According to that equation (and regressions in general), if you just increased (ability) by 1, what changes isn't (family income), it's the dependant variable (child income). I let you figure out exactly how much is changes by. But that's the point of the regressions, you're creating an equation which lets you figure out what happens to the dependant variable, when you change just one if the independent variables. The independent variables don't affect one another, that's why they're independent.


The same goes for changing (family income) by a single unit too. Try to figure out how much the dependant variable changes when you just increase family income by $1. As with (ability) above, finding out how the dependant variable changes is just a matter of using multiplication to see how the dependant variable changes.

Once you've done that, then you'll need to see whether the coefficients you've obtained are statistically significant; use the t and/or p values for this.

freeze4real

andrew wrote: »

The first number, without any coefficient, is the intercept. It tells you how much a person would earn, if the other two coefficients were 0 (according to the data you have).

Whatever book you're using should a have a specific bit on interpreting the numbers in front of the coefficients, but to offer some explanation:

Remember, the point of a regression is to try to figure out what factors affect some other factor of interest. The factor you're interested in is called the dependant variable, and the other factors which you think might affect the dependant variable are the independent variables.

In your case, child's income is the dependant variable, and family income and ability are the independent variables. I figure you probably already have an idea of this already, all you need to do now is relate this to the equation above.

Imagine, then, the output of that equation when you change (ability) by a single unit; you said that that affects (family income). But how? According to that equation (and regressions in general), if you just increased (ability) by 1, what changes isn't (family income), it's the dependent variable (child income). I let you figure out exactly how much is changes by. But that's the point of the regressions, you're creating an equation which lets you figure out what happens to the dependent variable, when you change just one if the independent variables. The independent variables don't affect one another, that's why they're independent.


The same goes for changing (family income) by a single unit too. Try to figure out how much the dependent variable changes when you just increase family income by $1. As with (ability) above, finding out how the dependent variable changes is just a matter of using multiplication to see how the dependent variable changes.

Once you've done that, then you'll need to see whether the coefficients you've obtained are statistically significant; use the t and/or p values for this.

I have the principles of economics book 4th edition. but I have only studied chapter 1 and 2.

Thanks for taking the time to explain it.

I'll do the first which is to see how a change in the independent variable affects the dependent variable.

Helpneeded86

Im a bit confused by this and would appreciate some help.

Y= B0 + B1(X1) + B2(X2) + B3(X3)

Lets say B0 is the intercept is that correct?

B1, 2 and 3 are the independent variables.

Assuming i have the above correct what confuses me is what is X1,2,3?


Also assuming the following question

Write out the appropriate Demand/Sales equation and comment on the value of the coefficients of the individual terms in the regression equation. You should also describe what each term means with respect to the overall demand/sales for/of coffee.

Is the above equation what i should be writing out

Y= 7.84 + 0.301(X1) + 0.27(X2)

What figures would you fill in for X is what still confuses me.

Helpneeded86

Anyone?

Adhamh

What a fluke, I'm studying this as well right now. I'm not one to answer these questions myself, but I found this video very useful:

http://www.youtube.com/watch?v=XvjYh1nuGos&list=UU8af2IlJZPDO-1McltpWDoQ&index=11&feature=plcp

andrew

Helpneeded86 wrote: »

Im a bit confused by this and would appreciate some help.

Y= B0 + B1(X1) + B2(X2) + B3(X3)

Lets say B0 is the intercept is that correct?

B1, 2 and 3 are the independent variables.

Assuming i have the above correct what confuses me is what is X1,2,3?


Also assuming the following question

Write out the appropriate Demand/Sales equation and comment on the value of the coefficients of the individual terms in the regression equation. You should also describe what each term means with respect to the overall demand/sales for/of coffee.

Is the above equation what i should be writing out

Y= 7.84 + 0.301(X1) + 0.27(X2)

What figures would you fill in for X is what still confuses me.

X1 and X2 in the second equation are the factors which might affect the demand for coffee. The numbers in front of X1 and X2 tell you the direction of the effect these factors have (can be positive or negative) as well as the magnitude of the effect.

Helpneeded86

andrew wrote: »

X1 and X2 in the second equation are the factors which might affect the demand for coffee. The numbers in front of X1 and X2 tell you the direction of the effect these factors have (can be positive or negative) as well as the magnitude of the effect.

Ok so in my example the intercept was coffee consumption and its co efficient was 2.52.

There was 3 ind variables price(-1.10),income(0.003) and temperature(0.031).

So Y= 2.52 -1.10(Price) + 0.003(income) + 0.031(temp)

Is the above correct so?

b Write out the appropriate Demand/Sales equation and comment on the value of the coefficients of the individual terms in the regression equation. You should also describe what each term means with respect to the overall demand/sales for/of coffee.

I need to study a little more about how to comment on each factor.

I understand how the price has a huge effect but on a negative confuses me i assume this means that when they raise the price of coffee it has a negative impact on sales.

The other two factors have very little bearing on sales.


In past examples it was a little easier

eg:

Salary 12226 = intercept

+ ind var years of education 1234

12226 + 1234( years of edu)

The above makes sense to me.

The coffee example does not

2.52 - 1.10(price)

Sorry if im missing something very simple here.

andrew

Helpneeded86 wrote: »

I need to study a little more about how to comment on each factor.

I understand how the price has a huge effect but on a negative confuses me i assume this means that when they raise the price of coffee it has a negative impact on sales.

The other two factors have very little bearing on sales.

Aye, you're on the right track here.

Helpneeded86

I thought i understood the F test and significant F test until i encountered this.

I use the Tables to see if they can pass. The significant F is then the level which they will pass at is it not?

Im just confused when i get this as an answer 1.48008E-08.

Edit: help received im ok thanks.