Read the following description of a data set.Faced with budget cuts, a state commission is looking into closing some of its public libraries. To help minimize the negative impact of the closures, the commission gathered data on local school and library facilities.The number of schools, x, and the number of libraries, y, were recorded for each town.The least squares regression line of this data set is:y=0.084x+1.743How many libraries does this line predict for a town with 5 schools?Round your answer to the nearest integer. libraries
Question
Read the following description of a data set.Faced with budget cuts, a state commission is looking into closing some of its public libraries. To help minimize the negative impact of the closures, the commission gathered data on local school and library facilities.The number of schools, x, and the number of libraries, y, were recorded for each town.The least squares regression line of this data set is:y=0.084x+1.743How many libraries does this line predict for a town with 5 schools?Round your answer to the nearest integer. libraries
Solution
To find the predicted number of libraries for a town with 5 schools, we need to substitute x = 5 into the equation of the least squares regression line.
The equation is y = 0.084x + 1.743.
Substituting x = 5, we get:
y = 0.084(5) + 1.743 y = 0.42 + 1.743 y = 2.163
Rounding to the nearest integer, we get 2.
So, the line predicts that a town with 5 schools will have 2 libraries.
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