Question

A study was done to investigate the use of text messaging over time. The correlating linear model is shown, where x represents the number of years after 2006, and y represents the average number of text messages a person sends monthly. Interpret the y-intercept.

A.

In 2006, a person sent an average of 65 text messages per month.

B.

In 2005, a person sent an average of 146 text messages per month.

C.

In 2005, a person sent an average of 65 text messages per month.

D.

In 2006, a person sent an average of 146 text messages per month.

Answer 1

Correct option: (A)

Explanation:

The correlating linear model to investigate the use of text messaging over time is:

`y=146x+65`

The general simple linear regression line is given by,

`y=\alpha +\beta x`

Here,

α = intercept of y,

β = slope (or regression) coefficient,

X = independent variable = number of years after 2006

Y = dependent variable = average number of text messages a person sends monthly.

The given regression line (or estimating line) is,
`y=146x+65`.

The y-intercept is the expected mean value of Y when X = 0.

Compute the y-intercept as follows:

`y=146x+65\\`

`=(146* 0)+65\\=0+65\\=65`

So, the y-intercept of 65 implies that in 2006 the average number of texts sent by a person is 65 texts per month.

Thus, the correct option is (A).