The necessary calculations done below, where x: Cups of coffee, y=People
a) b= sum(s3)/sum(s1) = Sxy/Sxx= -36.25/18.8748 = -1.920
here xbar= mean(x) = 3.125 , ybar=mean(y)=7.25
a= ybar-b*xbar = 7.25 -(-1.920)*(3.125) = 13.252
Therefore linear eqaution of yhat is
yhat= 13.252 -1.920*x
b) Correlation coefficient(r)
r= sum((x-xbar)*(y-ybar))/ sqrt(sum((x-xbar)^2)*sum((y-ybar)^2) = sum(s3)/sqrt(sum(s1)*(sum(s2))
= -36.25/ sqrt(18.8748*73.5)
r=-0.9732
c) r= -0.9732, suggest that there is strong linear trend.
d) slope=b= -1.920 , When unit change in number of coffee cups we expect the people that complain about profeesor's attitude will decreases by 1.92.
e) intercept= a= 13.252, When there no coffee cups then we expect the on average there are 13.252 people that complain about profeesor's attitude.
f) The number of coffee cups is the 8 then the predicted people is
yhat= 13.252 -1.920*x
yhat= 13.252 -1.920*8
=-2.1126
The number of coffee cups is the 8 then the predicted people that complain about profeesor's attitude is -2.1126
g) The prediction is not resonable, beacuse value of number of people is never negative.
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