Question

10 betagsautosaven4341927.11 wa Mal WOULON Cangan hudent Solution The following table shows on werage per capita wine consumption and heart disease reper 100.000 people in a random sample of 10 countries Yearty wine consumation Inters 2.5 2.9 3.4 2.0 08 27 0.8 02 Death from heart diseases 221 190 295 75 173 212 191 These datorer of where the deather de per 100.000 The India Part 0.7,301 Therman OH PO MacBook 3 4 R P S F Н. J K С B N M

Answer 1

Let x=yearly wine consumption in liters, y=death from heart diseases

Part a: The slope indicates that for each additional liter of wine consumed per capita, the heart disease death rate will decrease by 23.9 deaths per 100000 people. The y intercept indicates that when no wine is consumed, the expected heart disease death is 266.8 deaths per 100000 people.

Part b: Answer: (2.9, 132) (since corresponding residual=-65.482602 which is largest).

The residual means that when wine consumption is at 2.9 liters, the observed number of deaths is 65.48 fewer than the predicted value. Receving this data point below the regression line, so it is an outlier and it is an influential point.

Part c:

$H_0:\rho=0\\ H_1:\rho\neq 0.$

r=-0.84

p-value=0.0024

Option: p-value<0.010.

Option: Reject H₀. There is enough evidence to support the claim that there is a linear association between wine consumption and heart disease death rate.

R code:

x=c(2.5,3.9,2.9,2.4,2.9,0.8,9.1,2.7,0.8,0.7)
y=c(221,167,132,190,219,296,71,173,212,301)
lm(y~x)#(a)
d=data.frame(cbind(x,y,resid(lm(y~x))))
d#(b)
#(c)
round(cor(x,y),2)
n=length(x)
r=cor(x,y)
round(2*(1-pt(abs((sqrt(n-2)*r)/sqrt(1-r^2)),n-2)),4)#p-value