vv A second hand car dealer has ten cars

2022-03-09 Answered

vv

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car.

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car.

A second hand car dealer has ten cars for sale. He decides to investigate the link between the

ages of the cars, x years and the mileage, y thousand miles. The data collected from the cars

are shown in the table below.

Age, x years

2 2.5 3 4 4.5 4.5 5 3 6 6.5

Mileage, y thousand miles

22 34 33 37 40 45 49 30 58 58

(a) Construct a well labeled scatter diagram in the graph paper provided to present the

information. (3 marks)

(b) Find Sxx and Sxy. (3 marks)

(c) Find the regression equation in the form y = α + βx. (4 marks)

(d) Fit the regression equation obtained in (c) to the scatter plot in (a) and label the line

appropriately. (2 marks)

(e) Give a practical interpretation of the slope β. (1 mark)

(f) Using your answer in (c), fifind the mileage for a 6 year old car

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Answers (1)

nick1337
Answered 2022-03-22 Author has 510 answers

Equation of regression line is Y^=a+bX

b=n XY- X Yn X2-( X)2
b=10*1818.5-41*40610*188-(41)2
b = 7.734


a= Y-(b* X)n
a =406 - ( 7.7337 * 41 )10
a = 8.892
Equation of regression line becomes Y^=8.892+7.7337X

 

When X = 5
Y^= 8.892 + 7.734 X
Y^= 8.892 + 7.734 * 5
Y^ = 47.56

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