Question

the table below shows the average sat math scores from 1993-2002.

year	sat math scores
1994	504
1995	506
1996	508
1997	511
1998	512
1999	511
2000	514

using the data from the table determine if there is a linear trend between the year and the average sat math scores and determine if there is an exact linear fit of the data. describe the linear trend if there is one.

a. positive linear trend, an exact linear fit.

b. positive linear trend, not an exact linear fit.

c. negative linear trend, not an exact linear fit.

Explanation:

1. First, analyze the trend of SAT math scores over the years: From 1993 (503) to 2000, most scores are increasing (1993:503, 1994:504, 1995:506, 1996:508, 1997:511, 1998:512, 1999:511, 2000:514). So there is a positive trend.
2. Then, check for exact linear fit: In a linear fit, the difference between consecutive scores should be constant (slope constant). Let's calculate the differences:

• 1994 - 1993: \(504 - 503 = 1\)
• 1995 - 1994: \(506 - 504 = 2\)
• 1996 - 1995: \(508 - 506 = 2\)
• 1997 - 1996: \(511 - 508 = 3\)
• 1998 - 1997: \(512 - 511 = 1\)
• 1999 - 1998: \(511 - 512 = -1\)
• 2000 - 1999: \(514 - 511 = 3\)

The differences are not constant, so it's not an exact linear fit.

Answer:

b. Positive linear trend, not an exact linear fit.