In: Statistics and Probability
Using the following data set:
Observation Brand Price ($)
Megapixels Weight (oz.) Score
1 Canon 330 10
7 66
2 Canon 200 12
5 66
3 Canon 300 12
7 65
4 Canon 200 10
6 62
5 Canon 180 12
5 62
6 Canon 200 12
7 61
7 Canon 200 14
5 60
8 Canon 130 10
7 60
9 Canon 130 12
5 59
10 Canon 110 16
5 55
11 Canon 90 14
5 52
12 Canon 100 10
6 51
13 Canon 90 12
7 46
14 Nikon 270 16
5 65
15 Nikon 300 16
7 63
16 Nikon 200 14
6 61
17 Nikon 400 14
7 59
18 Nikon 120 14
5 57
19 Nikon 170 16
6 56
20 Nikon 150 12
5 56
21 Nikon 230 14
6 55
22 Nikon 180 12
6 53
23 Nikon 130 12
6 53
24 Nikon 80 12
7 52
25 Nikon 80 14
7 50
26 Nikon 100 12
4 46
27 Nikon 110 12
5 45
28 Nikon 130 14
4 42
10. Test whether price and score are correlated, using level of significance ? = 0.01
11. Test for the significance of the relationship between price and score, using level of significance ? = 0.01.
12. Construct and interpret a 90% confidence interval for the slope of the population regression line between price and score.
The correlation coefficient between the Price$ and Score is = 0.683
Our
x<-c(330,200,300,200,180,200,200,130,130,110,90,100,90,270,300,200,400,120,170,150,230,180,130,80,80,100,110,130)
y<-c(66,66,65,62,62,61,60,60,59,55,52,51,46,65,63,61,59,57,56,56,55,53,53,52,50,46,45,42)
cor.test(x,y)
plot(x,y,xlab = "Price",ylab = "Score",main="Price Score
Relationship")
model<-lm(y~x)
summary(model)
abline(model)
#90% confidence interval of slope
confint(model, 'x', level=0.90)
The 95% confidence interval for the slope is the estimated coefficient (0.05525) ± two standard errors (0.01158).