Devin creates a table showing five points. He uses a spreadsheet calculator to calculate the slope and y intercept of the least squares regression line based on the points in the table what is the slope of this line

Table
x y
0 12
1 14
2 16
3 18
4 20

1 answer

To find the slope of the least squares regression line for the given points, we can use the formula for the slope m:

m=N(xy)(x)(y)N(x2)(x)2

Where:

  • N is the number of points,
  • xy is the sum of the product of each x and y,
  • x is the sum of all x values,
  • y is the sum of all y values,
  • x2 is the sum of the squares of each x value.

Given your data points:

  • (0,12)
  • (1,14)
  • (2,16)
  • (3,18)
  • (4,20)

We first calculate the required sums:

  1. Calculating x, y, xy, and x2:

x=0+1+2+3+4=10

y=12+14+16+18+20=80

xy=(012)+(114)+(216)+(318)+(420)=0+14+32+54+80=180

x2=(02)+(12)+(22)+(32)+(42)=0+1+4+9+16=30

  1. Calculating N:

N=5

  1. Now plug into the slope formula:

m=5(180)(10)(80)5(30)(10)2 m=900800150100 m=10050=2

Therefore, the slope of the least squares regression line based on the given points is 2.