Question

Age and Price data for a sample of 12 cars

Age (years)            5       4       5          5      7      6      6       2       7        7        8      9

Price(Hundreds)   95    100   75        82    89    98     66      95    179     72      49    84

At the 1% significance level do the data provides sufficient evidence to conclude that age and price of cars are negatively correlated. a) Perform a hypothesis test ( 6 points)

1. State Null and alternative Hypothesis

2. Test Statistics

3. P-value approach

4. Conclusion:

2. Find the line of best-fit (2 points)

3. Explain what is in terms of age and price.( 2 points)

Answer 1

(For computing correlation, I have used R code:

x=c(5,4,5,5,7,6,6,2,7,7,8,9)
y=c(95,100,75,82,89,98,66,95,179,72,49,84)
#x=Age, y=Price
round(cor(x,y),4)

)

For finding regression equation I have used R code:

x=c(5,4,5,5,7,6,6,2,7,7,8,9)
y=c(95,100,75,82,89,98,66,95,179,72,49,84)
#x=Age, y=Price
m=lm(y~x)
round(m$coefficients,4)
m1=lm(x~y)
round(m1$coefficients,4)