8.2 Baby weights, Part II. Exercise 8.1 introduces a data set on birth weight of babies. Another variable we consider is parity, which is 0 if the child is the first born, and 1 otherwise. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, from parity. Estimate Std. Error t value Pr(>|t|) (Intercept) 120.07 0.60 199.94 0.0000 parity -1.93 1.19 -1.62 0.1052 (a) Write the equation of the regression line. Answer: birth weight of baby = 120.07 - 1.93 X parity

  1. Interpret the slope in this context, and calculate the predicted birth weight of first borns and others.

Answer: Intercept of 1207.07 indicates that when the parity is zero, that means the child is first born, the wight of the baby will be 120.07 ounces.

  1. Is there a statistically significant relationship between the average birth weight and parity? Answer:

Null Hypothesis: H0 : NO RELATIONSHIP OR SLOPE = 0 Alternate Hypothesis: HA: relationship is there, or slope not = 0

As we see from the data given, p-value = 0.1 As p-value > 0.05 (the general value of significance level), the null hypothesis cannot be rejected. That means there is no statistical relationship between the 2.

8.4 Absenteeism. Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from 146 randomly sampled students in rural New SouthWales, Australia, in a particular school year. Below are three observations from this data set. eth sex lrn days 1 0 1 1 2 2 0 1 1 11 … … … … … 146 1 0 0 37 The summary table below shows the results of a linear regression model for predicting the average number of days absent based on ethnic background (eth: 0 - aboriginal, 1 - not aboriginal), sex (sex: 0 - female, 1 - male), and learner status (lrn: 0 - average learner, 1 - slow learner).18 Estimate Std. Error t value Pr(>|t|) (Intercept) 18.93 2.57 7.37 0.0000 eth -9.11 2.60 -3.51 0.0000 sex 3.10 2.64 1.18 0.2411 lrn 2.15 2.65 0.81 0.4177 (a) Write the equation of the regression line.

Answer: number of days absent = 18.93 - 9.11 X eth + 3.10 X sex + 2.15 X lrn

  1. Interpret each one of the slopes in this context. Answer: ethnic background: a student with non-aboriginal background is estimated to be absent 9.11 days less as compared to a student with aboriginal background

sex: a male student is predicted to be 3.1 days less absent as compared to a female student, on an average

lrn: a slow learner is predicted to be 2.15 days less absent on an average as compared to an average learner

  1. Calculate the residual for the first observation in the data set: a student who is aboriginal, male, a slow learner, and missed 2 days of school. Answer: Using the equation from answer a above: number of days absent = 18.93 - 9.11 X eth + 3.10 X sex + 2.15 X lrn = 18.93 - 9.11 X 0 + 3.10 X 1 + 2.15 X 1 = 24.18

RESIDUAL = 2 - 24.18 = -22.18

  1. The variance of the residuals is 240.57, and the variance of the number of absent days for all students in the data set is 264.17. Calculate the R2 and the adjusted R2. Note that there are 146 observations in the data set. Answer:
R_squared <- 1 - (240.57 / 264.17)
R_squared
## [1] 0.08933641
R_squared_adj <- 1 - ((240.57 / 264.17) * (146 - 1)/(146-3-1))
R_squared_adj
## [1] 0.07009704

8.8 Absenteeism, Part II. Exercise 8.4 considers a model that predicts the number of days absent using three predictors: ethnic background (eth), gender (sex), and learner status (lrn). The table below shows the adjusted R-squared for the model as well as adjusted R-squared values for all models we evaluate in the first step of the backwards elimination process. Model Adjusted R2 1 Fullmodel 0.0701 2 Noethnicity -0.0033 3 Nosex 0.0676 4 No learner status 0.0723 Which, if any, variable should be removed from the model first?

Answer: As we see in the above data, removing learner status increases the R squared value as compared the full model, so learner status should be removed first