Question

The equation for the line of best fit for a data set is y = 2x + 1.5. If the point (1, 4) is in the data set, what is the residual of 1? 0.5 3.5 4.0 7.5

Answer 1

Answer: First option is correct.

Explanation:

Since we have given that

`y=2x+1.5`

If the point (1,4) is in the data set.

we need to find the residual of 1.

At x = 1,

`y=2x+1.5\\\\y=2* 1+1.5\\\\y=2+1.5\\\\y=3.5`

So, At x = 1, the value of y = 3.5

As we know that

`Residual\ value=Estimate\ value-Actual\ value\\\\Residual\ value=4-3.5\\\\Residual\ value=0.5`

Hence, The residual of 1 is 0.5.

Thus, First option is correct.

Answer 2

It is related to econometrics, however using simple algebraic logic we can solve this problem. General formula with residual is
`y=2x+1.5+r`, where r is a residual. Plugging the pair into the formula, we obtain that
`4=2*1+1.5+r` and r=0.5