Respuesta :
The equation for the least-squares regression line for the number of assaults compared with the number of robberies is 309,459.42+1.31x
What is mean?
⇒ Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
What is the standard deviation?
⇒ A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
⇒ Least square regressions are used to find the equation of best fit between two variables.
Calculation:
⇒ The number of robberies in the US in 2000 is x=354,718 and in 2005 is y=774,140
Mean, x=354,718 y=774,140
Standard deviation sx=28,803 sy=44,910
The correlation coefficient is r=0.84
⇒The regression coefficient of y and x is
[tex]b_{yx}[/tex]=[tex]x.\frac{s_{x} }{s_{y} }}[/tex]
=0.84×44910/28803
=1.3097≈1.31
Let the required regression(Y) line be
Y= A+[tex]b_{yx}[/tex]
Y=A+1.31x
⇒ A=Y-1.31x
∴ a=x-1.31x (here x is mean)
=774,140-1.31×354,718
=309,459.42
⇒ Hence the required regression line is 309,459.42+1.31x
Learn more about Least square regression here :
brainly.com/question/2141008
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