Lab Assignment 3

Estimate a multiple regression model where reading achievement scores (read) are regressed on highest grade completed by child’s mother (medu), whether child was breastfed (breastfed), and whether a child was born low birth weight (bthwht)

Sys.setlocale("LC_ALL","English")

[1] "LC_COLLATE=English_United States.1252;LC_CTYPE=English_United States.1252;LC_MONETARY=English_United States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252"

setwd("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 3")
NLSY <- read.csv("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 3/NLSY-2.csv")
Mod1 <- lm(read~medu+breastfed+bthwht,data=NLSY)
summary(Mod1)

Call:
lm(formula = read ~ medu + breastfed + bthwht, data = NLSY)

Residuals:
    Min      1Q  Median      3Q     Max 
-50.093  -8.618   0.382   9.148  39.360 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  80.0022     1.3612  58.773  < 2e-16 ***
medu          1.7375     0.1065  16.308  < 2e-16 ***
breastfed     3.8161     0.5305   7.193 7.99e-13 ***
bthwht       -1.9803     0.9705  -2.041   0.0414 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.95 on 2972 degrees of freedom
Multiple R-squared:  0.1217,    Adjusted R-squared:  0.1208 
F-statistic: 137.3 on 3 and 2972 DF,  p-value: < 2.2e-16

Q1: What proportion of the variation in the dependent variable is explained by the independent variables (R2)?

A1: 12%

Q2: What is the, on average, estimated mean reading achievement score when the independent variables are equal to 0 (intercept)?

A2: 80

Q3: Interpret the unstandardized coefficient for the breastfed variable.

A3: An increase of 1 unit in the breastfed variable results, on average, in an increase of 3.8 units in dependent variable (read).

Q4: Using the modelEffectSizes() function in the lmSupport package, produce a Semipartial and partial correlation table.

install.packages("lmSupport")

WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:

https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/Qiu J/Documents/R/win-library/4.1’
(as ‘lib’ is unspecified)
trying URL 'https://cran.rstudio.com/bin/windows/contrib/4.1/lmSupport_2.9.13.zip'
Content type 'application/zip' length 181439 bytes (177 KB)
downloaded 177 KB

package ‘lmSupport’ successfully unpacked and MD5 sums checked

The downloaded binary packages are in
    C:\Users\Qiu J\AppData\Local\Temp\RtmpkxlbXV\downloaded_packages

library(lmSupport)

Warning: package ‘lmSupport’ was built under R version 4.1.1
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     

modelEffectSizes(Mod1)

lm(formula = read ~ medu + breastfed + bthwht, data = NLSY)

Coefficients
                    SSR df pEta-sqr dR-sqr
(Intercept) 672341.5861  1   0.5375     NA
medu         51762.2586  1   0.0821 0.0786
breastfed    10070.5752  1   0.0171 0.0153
bthwht         810.4742  1   0.0014 0.0012

Sum of squared errors (SSE): 578476.1
Sum of squared total  (SST): 658638.8

Rerun the model and use the scale() function to standardize the variables

NLSY$read_scale <- scale(NLSY$read)
NLSY$medu_scale <- scale(NLSY$medu)
NLSY$breastfed_scale <- scale(NLSY$breastfed)
NLSY$bthwht_scale <- scale(NLSY$bthwht)
Mod1_scale <- lm(read_scale~medu_scale+breastfed_scale+bthwht_scale,data=NLSY)
summary(Mod1_scale)

Call:
lm(formula = read_scale ~ medu_scale + breastfed_scale + bthwht_scale, 
    data = NLSY)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3667 -0.5792  0.0256  0.6148  2.6453 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      1.070e-16  1.719e-02   0.000   1.0000    
medu_scale       2.892e-01  1.774e-02  16.308  < 2e-16 ***
breastfed_scale  1.282e-01  1.783e-02   7.193 7.99e-13 ***
bthwht_scale    -3.533e-02  1.732e-02  -2.041   0.0414 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9376 on 2972 degrees of freedom
Multiple R-squared:  0.1217,    Adjusted R-squared:  0.1208 
F-statistic: 137.3 on 3 and 2972 DF,  p-value: < 2.2e-16

Q5: Interpret the standardized coefficient for the medu variable.

A5: An increase of 1 standard deviation in medu results, on average, in an increase of 0.289 standard deviation in dependant variable (read).