The annual profits for a company are given in the following table, where x represents the number of years since 2006, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the projected profit (in thousands of dollars) for 2015, rounded to the nearest thousand dollars.

The linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth is: y=13.35x+59.81 and the projected profit is $179.96.

Linear regression equation and projected profit

First step is to find the mean for x and y

x=0+1+2+3/4

x=1.25

y=69+75+75+87/4

y=306/4

y=76.5

Second step is to find the sum

b=(0×69+1×75+2×75+3×87)-(4×1.25×76.5)÷0²+1²+2²+3²-4×1.25²

b=13.35

Third step is to find the intercept a.

a=76.5-13.35×1.25

a=59.81

linear regression equation:

y=13.35x+59.81

Fourth step is to find the projected profit

x=2015-2006

x=9

Hence:

y=13.35x+59.81

y=13.35×9+59.81

y=$179.96

Therefore the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth is: y=13.35x+59.81 and the projected profit is $179.96.

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