The table below contains data on 10 cities: the explanatory variable is the population size in thousands, and the response variable is the number of car accidents per month. City 1 2 3 4 5 6 7 8 9 Population (in thousands) 75 85.5 68.75 82 94.25 105.5 73 59.75 125 87 Monthly Car Accidents 35 42 32 37 51 55 29 36 49 42 (1) Find the means and standard deviations of the two variables. (2) What is the correlation? (3) Write down the linear model in slope-intercept form
The table below contains data on 10 cities: the explanatory variable is the population size in thousands, and the response variable is the number of car accidents per month. City 1 2 3 4 5 6 7 8 9 Population (in thousands) 75 85.5 68.75 82 94.25 105.5 73 59.75 125 87 Monthly Car Accidents 35 42 32 37 51 55 29 36 49 42 (1) Find the means and standard deviations of the two variables. (2) What is the correlation? (3) Write down the linear model in slope-intercept form
The table below contains data on 10 cities: the explanatory variable is the population size in thousands, and the response variable is the number of car accidents per month. City 1 2 3 4 5 6 7 8 9 Population (in thousands) 75 85.5 68.75 82 94.25 105.5 73 59.75 125 87 Monthly Car Accidents 35 42 32 37 51 55 29 36 49 42 (1) Find the means and standard deviations of the two variables. (2) What is the correlation? (3) Write down the linear model in slope-intercept form
The table below contains data on 10 cities: the explanatory variable is the population size in thousands, and the response variable is the number of car accidents per month.
City 1 2 3 4 5 6 7 8 9
Population (in thousands)
75 85.5 68.75 82 94.25 105.5 73 59.75 125
87
Monthly Car Accidents
35 42 32 37 51 55 29 36 49 42
(1) Find the means and standard deviations of the two variables.
(2) What is the correlation?
(3) Write down the linear model in slope-intercept form
(4) How many car accidents would you predict occurs in a city with a population of 125,000? What is
the associated residual?
(5) How many car accidents would you predict occurs in a city with a population of 5,000? Is this a
good prediction? Explain.
(6) Interpret the slope of the linear model in the context of this scenario.
(7) Can we conclude that higher population causes more car accidents?
Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
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