Question

what is it?

how does it work? when given a table of values, follow the steps below:

to enter the table of values:

• hit stat, then enter
• enter x - values into ( l_1 ) column
• enter y - values into ( l_2 ) column

to find the line of best fit:

• hit stat
• arrow over to calc
• select #4, linreg (ax + b)
• hit enter

examples:

1. the information in the table below shows average temperature in northern latitudes:

latitude (( n^circ ))	0	10	20	30	40	50	60	70	80

a. find the line of best fit.

b. estimate the average temperature for a city with a latitude of ( 25^circ )

1. the information in the table shows the olympic 500 - meter men’s gold medal speed skating times since 1980.

year	time (s)
1984	432
1988	404
1992	420
1994	395
1998	382

a. find the line of best fit.

b. estimate the 500 - meter time for the 2012 olympics.

1. the information in the table shows sales for a certain retail department store (in billions of dollars)

year	1980	1985	1990	1994	1995	1996	1997	1998

a. find the line of best fit.

b. estimate the store sales for the year 2008.

Explanation:

Problem 1a: Find the line of best fit for Latitude vs Temperature

Step1: Enter data into calculator

Enter \( x \)-values (Latitude: \( 0, 10, 20, 30, 40, 50, 60, 70, 80 \)) into \( L_1 \) and \( y \)-values (Temp: \( 79.2, 80.1, 77.5, 68.7, 57.4, 42.4, 30.0, 12.7, 1.0 \)) into \( L_2 \).

Step2: Calculate linear regression

Use LinReg (\( ax + b \)) function. The calculator gives \( a \approx -0.906 \), \( b \approx 79.8 \). So the line of best fit is \( y = -0.906x + 79.8 \).

Step1: Substitute \( x = 25 \) into the line of best fit

Use \( y = -0.906(25) + 79.8 \).

Step2: Calculate the value

\( -0.906 \times 25 = -22.65 \), then \( -22.65 + 79.8 = 57.15 \).

Step1: Enter data into calculator

Let \( x \) be years since 1980 (so \( x: 0, 4, 8, 12, 14, 18 \)) and \( y \)-values (Time: \( 422, 432, 404, 420, 395, 382 \)) into \( L_2 \).

Step2: Calculate linear regression

LinReg gives \( a \approx -2.34 \), \( b \approx 423.5 \). So the line is \( y = -2.34x + 423.5 \) (where \( x \) is years since 1980).

Answer:

\( y = -0.906x + 79.8 \) (approximate, values may vary slightly with calculator precision)

Problem 1b: Estimate temperature at \( 25^\circ \) latitude