# significant variables

#### Snowy88

##### New Member
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.
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?

#### Snowy88

##### New Member
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.
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.

#### Snowy88

##### New Member
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.
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
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
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

#### Snowy88

##### New Member
I'm new to R, which is the program I am using along with the data found in the library.

#### mba

##### New Member
Plus check the AIC, BIC, and LLR for best model fit.

mba