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he sales of a company (in million dollars) for each year are shown in the table ...

Jul 4, 2024

he sales of a company (in million dollars) for each year are shown in the table below. x (year) 2005 2006 2007 2008 2009 y (sales) 12 19 29 37 45 Find the least square regression line y = a + bx b) Use the least squares regression line as a model to estimate the sales of the company in 2010.

Generated Graph

Solution by Steps

step 1

To find the least squares regression line, we first need to fit a linear model to the given data points: \{(2005, 12), (2006, 19), (2007, 29), (2008, 37), (2009, 45)\}

step 2

Using the Asksia-LL calculator, the linear fit model is determined to be

y = 8.4x - 16830.4

step 3

To estimate the sales of the company in 2010 using the least squares regression line, we substitute

x = 2010

into the equation

y = 8.4x - 16830.4

step 4

Calculating the value:

y = 8.4 \times 2010 - 16830.4 = 16884 - 16830.4 = 53.6

Answer

The estimated sales of the company in 2010 is 53.6 million dollars.

Key Concept

Least Squares Regression Line

Explanation

The least squares regression line is a method to find the best-fitting line through a set of points by minimizing the sum of the squares of the vertical distances of the points from the line.