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library(wooldridge)
data("bwght")
df <- bwght

##QUESTION 4i

intercept <- 119.77
slope <- -0.514

cigs_0 <- 0
bwght_0 <- intercept + slope * cigs_0
cigs_20 <- 20
bwght_20 <- intercept + slope * cigs_20

bwght_0
## [1] 119.77
bwght_20
## [1] 109.49
difference <- bwght_0 - bwght_20

difference
## [1] 10.28

INTERPRETATION:

Babies whose mothers smoke 20 cigarettes per day weigh 10.28oz less than babies whose mothers who smoke 0 cigarettes per day

4ii)

Not necessarily because there may also be other factors affecting the mothers that affect the birth weight of the babies that are not accounted for

4iii)

To predict a birth weight of 125 ounces, the “cigs” variable would have to be a negative number. There is no possible way to smoke a negative amount of cigarettes.

“cigs” would have to be equal to = -10.175

4iv)

range_bwght <- range(df$bwght, na.rm = TRUE)

range_bwght
## [1]  23 271

No. This doesn’t change anything because of the 85% of non-smoking mothers (total of 1180), the babies weights still vary below and above 125.

QUESTION C3

data("sleep75")

dg <- "sleep75"

m1 <- lm(sleep ~ totwrk, data = sleep75)

summary(m1)
## 
## Call:
## lm(formula = sleep ~ totwrk, data = sleep75)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2429.94  -240.25     4.91   250.53  1339.72 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 3586.37695   38.91243  92.165   <2e-16 ***
## totwrk        -0.15075    0.01674  -9.005   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 421.1 on 704 degrees of freedom
## Multiple R-squared:  0.1033, Adjusted R-squared:  0.102 
## F-statistic: 81.09 on 1 and 704 DF,  p-value: < 2.2e-16

C3 i)

coef(m1)
##  (Intercept)       totwrk 
## 3586.3769515   -0.1507458
nobs(m1)
## [1] 706
summary(m1)$r.squared
## [1] 0.1032874

C3 ii)

b1 <- coef(m1)["totwrk"]

change_sleep <- b1 * 120
change_sleep
##   totwrk 
## -18.0895

C7 i)

data("charity")

mean(charity$gift)
## [1] 7.44447
mean(charity$gift == 0) * 100
## [1] 60.00469

C7 ii)

mean(charity$mailsyear)
## [1] 2.049555
summary(charity$mailsyear)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.25    1.75    2.00    2.05    2.50    3.50