Subject Mathematics Statistics-R Programming

Question

Categorical Independent Variables
Dataset: daycare_cat.sav
Variables explanations:
ID
Reading: Kindergarten reading score
SES: Socioeconomic Status
Care: Type of pre-kindergarten non-parental care
1: relative care
2: non-relative care
3: center care
4: Head Start
Questions:
1. Use dummy variable coding with Head Start as the reference group.
a. Controlling for SES, does the type of care have a significant effect on Children’s reading score in kindergarten? (Explain it in detail)
b. Please interpret the estimated intercept and the regression coefficients, and their corresponding significance tests.
c. Compute the predicted means of reading for each type with average SES.
2. Use unweighted effects coding with relative care as the base group.
a. Controlling for SES, does the type of care have a significant effect on Children’s reading score in kindergarten? Compare the results with Question1(a).
b. Please interpret the estimated intercept and the regression coefficients, and their corresponding significance tests.
c. Compute the predicted means of reading for each type with average SES? Compare the results with question1(c).

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daycarecat <- read.table("daycarecat.csv",header=TRUE,sep=",")
daycarecat$CARE <- as.factor(daycarecat$CARE)
contrasts(daycarecat$CARE) <- contr.treatment(4, base = 4)
fit <- lm(Reading ~ CARE + SES,data=daycarecat)
summary(fit)
# Call:
# lm(formula = Reading ~ CARE + SES, data = daycarecat)
#
# Residuals:
#    Min      1Q Median      3Q    Max
# -14.260 -4.947 -0.715   4.186 16.690
#
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)   
# (Intercept) 19.6558    0.7833 25.095 < 2e-16 ***
# CARE1         0.9569    0.9664   0.990 0.322523   
# CARE2         2.0309    1.0412   1.951 0.051596 .
# CARE3         3.3183    0.8894   3.731 0.000209 ***
# SES          3.2751    0.3628   9.028 < 2e-16 ***...

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