Answer to Question #158606 in Statistics and Probability for SR2

Question

The relationship between age (X, in year) and the number of overseas holidays a year (Y) has been studied using simple linear regression sing the following model.

Yi = 0 + 1 Xi + ui

The following table shows the data of age and the number of overseas destinations for a random sample of 20 respondents.

Age (X)

62

57

40

49

67

54

43

65

54

41

No of overseas holiday (Y)

6

5

4

3

5

5

2

6

3

1

Age (X)

44

48

55

60

59

63

69

40

38

52

No of overseas holiday (Y)

3

2

4

5

4

5

4

2

1

3

The summary of the data is as follows where SST is the total sum of squares, SSR is the regression sum of squares.

Xi = 1060, Yi = 73, Xi2 = 57994, Yi2 = 311, XiYi = 4097,

SST = Σ(𝑌𝑖−𝑌̅)2 = 44.55, SSR = Σ(𝑌̂𝑖−𝑌̅)2 = 28.65

a) Find the estimated regression line 𝑌̂𝑖 = b0 + b1 Xi that links the age with the number of overseas holidays in a year.

b) Test whether coefficient b1 is statistically significant or not. Use 5% significant level.

c) Interpret the estimated slope coefficient, b1.

d) Suppose that Ah Huat is 50 years old, predict how many times he has gone overseas for a holiday?

e) Give one quantitative and one qualitative variable that are expected to affect the number of overseas holiday in a year.

Answer 1

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