Seminar 22/01
Anna Podolskaya
22/01/2021
knitr::opts_chunk$set(fig.width=12, fig.height=8, fig.path='Figs/',
echo=FALSE, warning=FALSE, message=FALSE, error = FALSE)Problem 1
Using regression modelling, find out how interest in politics, marital status, and age relate to trust in parliament.
- Show how you create your models and choose the best of them.
- Explore models with and without moderation.
## pol_int marit age trstparl
## Min. :0.0000 Divorced: 97 Min. :16.00 Min. : 1.000
## 1st Qu.:0.3300 Married : 52 1st Qu.:47.25 1st Qu.: 3.000
## Median :0.6600 Single :154 Median :67.50 Median : 6.000
## Mean :0.5036 Widowed :171 Mean :61.41 Mean : 5.249
## 3rd Qu.:0.6600 3rd Qu.:76.00 3rd Qu.: 7.000
## Max. :1.0000 Max. :94.00 Max. :11.000##
## Call:
## lm(formula = trstparl ~ pol_int, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9639 -1.9639 0.5258 2.0011 6.4764
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5236 0.2112 21.41 < 2e-16 ***
## pol_int 1.4403 0.3496 4.12 4.48e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.542 on 472 degrees of freedom
## Multiple R-squared: 0.03471, Adjusted R-squared: 0.03267
## F-statistic: 16.97 on 1 and 472 DF, p-value: 4.478e-05##
## Call:
## lm(formula = trstparl ~ pol_int + marit, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2467 -1.9655 0.2474 1.9752 6.4548
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.0136 0.3175 12.643 < 2e-16 ***
## pol_int 1.4532 0.3511 4.139 4.13e-05 ***
## maritMarried 0.4505 0.4356 1.034 0.3016
## maritSingle 0.5316 0.3297 1.612 0.1076
## maritWidowed 0.7799 0.3221 2.421 0.0158 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.534 on 469 degrees of freedom
## Multiple R-squared: 0.04672, Adjusted R-squared: 0.03858
## F-statistic: 5.746 on 4 and 469 DF, p-value: 0.0001604##
## Call:
## lm(formula = trstparl ~ pol_int + marit + age, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2716 -1.9593 0.2536 1.9124 6.4593
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.222583 0.598617 7.054 6.29e-12 ***
## pol_int 1.470600 0.353931 4.155 3.87e-05 ***
## maritMarried 0.426773 0.439748 0.970 0.3323
## maritSingle 0.459031 0.374103 1.227 0.2204
## maritWidowed 0.819944 0.336702 2.435 0.0153 *
## age -0.003355 0.008145 -0.412 0.6806
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.536 on 468 degrees of freedom
## Multiple R-squared: 0.04706, Adjusted R-squared: 0.03688
## F-statistic: 4.622 on 5 and 468 DF, p-value: 0.000397As for the additive models, the first one is the best (trstparl ~ pol_int), significance in interest in politics only.
Then I’ve tried to add interaction:
##
## Call:
## lm(formula = trstparl ~ pol_int * marit, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.1390 -1.8298 0.4323 1.8560 6.7438
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.2562 0.4496 7.242 1.84e-12 ***
## pol_int 2.8827 0.6982 4.129 4.32e-05 ***
## maritMarried 1.1170 0.8530 1.309 0.191022
## maritSingle 1.2101 0.5609 2.157 0.031479 *
## maritWidowed 2.2522 0.5872 3.836 0.000142 ***
## pol_int:maritMarried -1.2656 1.3426 -0.943 0.346335
## pol_int:maritSingle -1.2532 0.9189 -1.364 0.173268
## pol_int:maritWidowed -2.7929 0.9335 -2.992 0.002919 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.517 on 466 degrees of freedom
## Multiple R-squared: 0.06506, Adjusted R-squared: 0.05101
## F-statistic: 4.632 on 7 and 466 DF, p-value: 4.996e-05##
## Call:
## lm(formula = trstparl ~ pol_int * age, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.0369 -1.9416 0.5048 1.9560 6.5515
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.251108 0.606276 7.012 8.23e-12 ***
## pol_int 1.941057 1.113137 1.744 0.0819 .
## age 0.004699 0.009838 0.478 0.6332
## pol_int:age -0.008395 0.017406 -0.482 0.6298
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.546 on 470 degrees of freedom
## Multiple R-squared: 0.03524, Adjusted R-squared: 0.02908
## F-statistic: 5.722 on 3 and 470 DF, p-value: 0.0007489##
## Call:
## lm(formula = trstparl ~ pol_int * age + marit, data = df1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.2238 -1.9573 0.2782 1.9528 6.5389
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.947331 0.748313 5.275 2.04e-07 ***
## pol_int 2.119641 1.115287 1.901 0.0580 .
## age 0.001326 0.011162 0.119 0.9055
## maritMarried 0.415902 0.440398 0.944 0.3455
## maritSingle 0.458095 0.374355 1.224 0.2217
## maritWidowed 0.830716 0.337383 2.462 0.0142 *
## pol_int:age -0.010685 0.017410 -0.614 0.5397
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.538 on 467 degrees of freedom
## Multiple R-squared: 0.04783, Adjusted R-squared: 0.03559
## F-statistic: 3.91 on 6 and 467 DF, p-value: 0.0008015INTERPRETATION :
- 0 interest in politics and divorced - trust in parlament is higher by 3.2562
- interested in politics and divorced - (3.2562 + 2.8827) trust in parlament is higher by 6
- 0 interest in politics and single - trust in parlament is higher by 1.2
- 0 interest in politics and widowed - trust in parlament is higher by 2.3 BUT if they ARE interested in politics, their trust in parlament is LOWER by 2.8.
wider with pol_int=1: \(predicted value = 3.26 + 2.25 + 2.88 - 2.79\) \(pred trust = 3.26 + 2.25*Widowed + 2.88*pol - 2.79*Widowed*pol\)
PLOT:
NB:
важно обратить внимание на отрезок графика 0-0.5 interest in politics - там, где фиолетовое и красные области не пересекаются - атм значимое различие в поведении двух групп.
Standartized values:
##
## Call:
## lm(formula = trstparl ~ pol_int * marit, data = df1)
##
## Standardized Coefficients::
## (Intercept) pol_int maritMarried
## 0.00000000 0.37290156 0.13523258
## maritSingle maritWidowed pol_int:maritMarried
## 0.21954913 0.41897406 -0.09823463
## pol_int:maritSingle pol_int:maritWidowed
## -0.13841937 -0.33911387Then, work with the best-fitting model by answering the following questions:
- How much variance in trust in parliament can your best model explain?
- What are the relationships between the predictors and the outcome variables? Interpret the coefficients.
- Which continuous predictor is most tightly related to the outcome?