Write a linear regression equation for this set of data, rounding values to the nearest ten-thousandth where necessary.

Question

The mid-September statewide average gas prices, in dollars per gallon (y), for the year since 2000 (x), are given in the table below.

Year Since 2000 (x): | Price Per Gallon (y)

1 | 1.345

2 | 1.408

3 | 1.537

4 | 1.58

Write a linear regression equation for this set of data, rounding values to the nearest ten-thousandth where necessary.

Answer 1

Hello Dexter,

A linear equation consists of a slope and a y intercept value. It has the form y=mx+b. To find the slope of the line, you would need to use the formula (y2-y1)/(x2-x1). Pick any two points from the data set to use in this formula.

For instance, you could use these points:

1 | 1.345

2 | 1.408

year = x

gas price = y

(1.408-1.345)/(2-1)=0.063.

The slope is 0.063

Now solve for the y intercept (b): plug in the x and y coordinates for any point in the equation and solve for b.

y=mx+b.

choose : 1 | 1.345

(1.345)=0.063*(1)+b

1.345-0.063=b

b=1.282

So your equation would be y=0.063x+1.282