An investigation was carried out on 10 second-hand cars to explore the relationship between the age of the car, t years and the mileage, M thousand kilometres. The data collected from each car are shown in the following table. Age, t (years) 2 25 3 4 4.5 4.5 5 6.5 3 Mileage, M (thousands km) 25 36 32 40 42 45 50 55 30 58 Σt= 41, ΣΜ= 413 , Σ tM 1833 , Σt2= 188, ΣM2 18123 (a) Find the regression line M = a + bt for the given data and write down the equation of the line in 2 decimal places. (b) Interpret the value of the slope, b, to given context. (c) Calculate the product-moment correlation coefficient for the given data. Comment on the value. (d) A second-hand car dealer estimates the mileage for a 10 year-old car to be around 132 thousand kilometres. Is the estimation made reliable? State your reason. 6.
An investigation was carried out on 10 second-hand cars to explore the relationship between the age of the car, t years and the mileage, M thousand kilometres. The data collected from each car are shown in the following table. Age, t (years) 2 25 3 4 4.5 4.5 5 6.5 3 Mileage, M (thousands km) 25 36 32 40 42 45 50 55 30 58 Σt= 41, ΣΜ= 413 , Σ tM 1833 , Σt2= 188, ΣM2 18123 (a) Find the regression line M = a + bt for the given data and write down the equation of the line in 2 decimal places. (b) Interpret the value of the slope, b, to given context. (c) Calculate the product-moment correlation coefficient for the given data. Comment on the value. (d) A second-hand car dealer estimates the mileage for a 10 year-old car to be around 132 thousand kilometres. Is the estimation made reliable? State your reason. 6.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 24PFA
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Question
Answer the last question
Transcribed Image Text:5:17 1
1 Litmatch
parts may be reposted.
Step2
b)
Q) For vegression line. M = atbt,
b= ŹMt - 1(3M)(St)
n
(413).(4)
1833 -
188 - (41)2
» b = 7.02
and a= sM _bŹt
413. 7.02x 41
= 12.52
10
So the requession equation is-
M=12.52+7.024
) Inter pretatim of slope is -
If the age of the
the mileage of the car will increased by 7.02 (thous
ands km).
car is increased by a year then
Step3
c)
c) The product moment correlation coefficient is-
ŹMt - (2M).(3 t)
IS M)
1833 - I(413) ( 41)
= 0.9591
To
10
This indicale Posttive and strong relationship between Mand t.
IAWas thie solution halnful2
VX &
Transcribed Image Text:6.
An investigation was carried out on 10 second-hand cars to
explore the relationship between the age of the car, t years and
the mileage, M thousand kilometres. The data collected from
each car are shown in the following table.
Age, t (years)
2 2.5 3
4 4.5 4.5 5 6.5 3
Mileage, M
(thousands km)
25 36 32 40 42
45 50 55| 30 58
Σt= 41,ΣΜ = 413, ΣtM1833 , Σt2= 188, ΣΜ218123
(a)
Find the regression line M = a + bt for the given data and
write down the equation of the line in 2 decimal places.
(b) Interpret the value of the slope, b, to given context.
(c) Calculate the product-moment correlation coefficient for
the given data. Comment on the value.
(d) A second-hand car dealer estimates the mileage for a 10
year-old car to be around 132 thousand kilometres. Is the
estimation made reliable? State your reason.
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