significant variables

#1
I am working on a problem and need to determine the stat. significant variables and provide an interpretation on sex? I got the following results from my lm:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 22.55565 17.19680 1.312 0.1968
sex -22.11833 8.21111 -2.694 0.0101 *
area 0.05223 0.28111 0.186 0.8535
income 4.96198 1.02539 4.839 1.79e-05 ***
verbal -2.95949 2.17215 -1.362 0.1803
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 22.69 on 42 degrees of freedom
Multiple R-squared: 0.5267, Adjusted R-squared: 0.4816
F-statistic: 11.69 on 4 and 42 DF, p-value: 1.815e-06

In the results, sex and income are the most significant to the model. Is my conclusion correct and how would i interpret sex?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Does sex refer to gender? And if so did you enter it in as a categorical variable (e.g., 0/1 or m/f, etc.)? What is this for? Should you remove area and verbal from the model, or do you have to keep them in the model?
 
#3
sex is coded 0/1 and all variables have to be included. My prediction from the model is that on average female spend less than male with the same income.
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Sex is a significant predictor of spending when controlling for area, income, and verbal; with females spending on average $22.12 (95% CI: ??.??, ??.??; p-value: 0.0101) less than males.
 
#5
that was my next question, how do I calculate the 95% CI to predict the amount male spend with average on all variables ? do i still use my linear model?
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Are you using a statistical program? You may be able to activate that feature on your output. Our you can get at them with the standard error.
 

ledzep

Point Mass at Zero
#7
The output says that in average female spend less than males[taking male as ref category].

If I had extra time, out of interest, I will also look at any interaction between gender and income. i.e. Females with low income still spend more? or the uneconomical females are the ones with high income only.

[NB:What is your response? Is the average monthly expenses? If they are average expenses and if the average for each individual comes from an unequal #of observations, then weighted least squares would be the most appropriate. But you will be just as fine if they have equal number of observations]
 

mba

New Member
#8
To test about the significant variables:
1) build a logit of logit(y/1-y)=exp(B0+sex*B1 +Income*B3)/(1+exp(B0+sex*B1 +Income*B3)
a reduced model for fixed values and compare to the full model:

logit(y/1-y)=exp(B0+sex*B1 +B2*Area+Income*B3+Verbal*B4)/(1+exp(B0+sex*B1 +B2*Area+Income*B3+Verbal*B4)

test to see if the full model is more significant or the reduced with only significant values.
1b) The p values in the model might change also if you rerun it the model.

2) since the sex variable is -22.11 one might state that the impact of sex is to reduce by -22.11.. for model outcome for full model with the other parameters in the model. The actual value will change by the model selected and P value again.

3) T=Beta/S.E.

Thank you,
mba