Question

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 on dollars, Write all linear regression equation that represents this set data,rounding all coefficient to the nearest hundredth.Using this equation find the projected profit (in thousands of dollars) for 2015,rounded to the nearest thousand dollars x=0,1,2,3,4 y=137,135,171,165,202

Answer 1

The answer is very simple. .

To facilitate the calculations we must build a table.

We can use excel or you can also do it manually with the calculator.

I'll do it in excel and I'll share it with you

We will use this table to apply the necessary equations.

n = number of data we have in the table

n = 5

We substitute the values of the table in the equation to calculate a

`a\text{ = }(5\cdot1780-10\cdot810)/(5\cdot30-(10)^2)`

a = 800 / 50

a = 16

we already find the value of a

`b\text{ = }(810-16\cdot10)/(5)`

b = 650/ 5

b = 130

Finally we substitute in the equation

`y\text{ = 16x +130}`

The projected profit for 2015 would be

y = 16 *(9) + 130

y = 274 (thousands of dollars)