The accompanying data represent the weights of various domestic cars and their g
ID: 3366895 • Letter: T
Question
The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is
requals=negative 0.987?0.987.
The? least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is
ModifyingAbove y with caret equals negative 0.0076 x plus 46.4842y=?0.0076x+46.4842.
Complete parts ?(a) through? (c) below.
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?(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per? gallon?
The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is
nothing?%.
?(Round to one decimal place as? needed.)
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Data Table
Full data set
Car
Weight? (pounds), x
Miles per?Gallon, y
Car
Weight? (pounds), x
Miles per?Gallon, y
Car 1
?3,765
1818
Car 7
?2,605
2626
Car 2
?3,984
1717
Car 8
?3,772
1717
Car 3
?3,530
2020
Car 9
?3,310
2121
Car 4
?3,175
2222
Car 10
?2,991
2525
Car 5
?2,580
2727
Car 11
?2,752
2626
Car 6
?3,730
18
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Explanation / Answer
we find the coefficient of determination or r-sq
we know that rsq~ (correlation)^2
so R-sq = (-0.987)^2 =0.974169
so, 97% of varaibility in y is expalined by x
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