Question

The table and scatter plot show the time spent texting, x, and the time spent exercising, y, by each of 9 students last week.The equation of the line of best fit is y = - 0.4x + 6.96 .

Answer 1

Step-by-step explanation

We define the variables:

• x = time spent texting (in hours),

,

• y_O = observed time spent exercising (in hours),

,

• y_P = predicted time spent exercising (in hours).

,

• r = residual (in hours) = y_O - y_P.

From the statement, we have the following equation for the line of best fit:

`y_P=-0.4x+6.96.`

1) For x = 4.0 we have:

• y_O = 4.50 (from the table),

,

• y_P = 5.36 (by using the formula),

,

• r = 4.50 - 5.36 = 0.86.

2) For x = 5.0 we have:

• y_O = 6.50 (from the table),

,

• y_P = 4.96 (by using the formula),

,

• r = 6.50 - 4.96 = 1.54.

Answer

1) For x = 4.0 we have: y_O = 4.50, y_P = 5.36, r = -0.86

2) For x = 5.0 we have: y_O = 6.50, y_P = 4.96, r = 1.54