Question

In: Statistics and Probability

Using the following data set: Observation   Brand   Price ($)   Megapixels   Weight (oz.)   Score 1   Canon   330  ...

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.

Solutions

Expert Solution

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).


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