SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table 12.4 show different depths with the maximum dive times in minutes. Use your calculator to find the least-squares regression line and predict the maximum dive time for $110$feet.

X (depth in feet)	Y (maximum dive time)
50	80
60	55
70	45
80	35
90	25
100	22

The least squares regression line can be written as shown below:

$\overline{y}=a+b\overline{x}$

Here, intercept $a$can be calculated by the formula shown below:

$a=\overline{y}-b\overline{x}$

And, slope $b$can be calculated by the formula shown below:

$b=\frac{\sum (x-\overline{x})(y-\overline{y})}{\sum (x-\overline{x}{)}^2}$

The data referred in the textbook.

Do calculations in excel worksheet as shown below:

Calculate the average of variable $x$and $y$by using $=AVERAGE$function of excel as shown below:

Make column of $(x-\overline{x})$and $(x-\overline{x}{)}^2$by subtracting $\overline{x}$from each observation of $x$and then take sum of columns $(x-\overline{x}{)}^2$as shown below:

Finally, make last column of $(x-\overline{x})\times (y-\overline{y})$by multiplying each value of column $(x-\overline{x})$and $(y-\overline{y})$and take the sum of column $(x-\overline{x})\times (y-\overline{y})$as shown below:

Substitute the value in the slope $b$formula as shown below:

$=\frac{-1950}{1750}$

$=-1.11$

Substitute the value in the intercept $a$formula as shown below:

$a=\overline{y}-b\overline{x}$

$=43.67-(-1.11)75$

$=127.24$

Hence, the least squares regression line is shown below:

$\overline{y}=a+b\overline{x}$

$\overline{y}=127.24+(-1.11)\overline{x}$

At $110$feet, a diver could dive only five minutes.

At $110$ feet, a diver could dive only five minutes.