Which equation of the least squares regression line most closely matches the data set?

note: the variable x represents the years after 1990.

data set below

x y

1990 45

1992 51

1994 57

1996 61

1998 75

1. y=5.5x+52

2. y=2.2x+13.8

3. y=3.5x+43.8

4. y=3.5x−43.8

y = 3.5 x+ 43.8

Step-by-step explanation:

Here x represents the number of years after 1990

Thus, we get the table that is used to find the equation will be,

x             0                  2                4               6                8

y             45                51               57            61               75

Let the equation that shows the above data,

y = b + a x ---------(1)

By the above table,

By substituting these values in the above value of a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equation (1)

we get, the equation that shows the given data is,

y = 3.5 x + 43.8

⇒ Option (3) is correct.

y = 3.5 x+ 43.8

Step-by-step explanation:

Verified correct with a K12 test.

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