In Mark Twains book Life on the Mississippi, he made a strange prediction about the future of the Mississippi River.The river is extremely crooked with many curves.From time-to-time cut-offs take place in which the river changes its course from a wide bend to a straighter path.As a result the length of the Mississippi is getting shorter.Twain gave some figures:The Mississippi between Cairo (Illinois) and New Orleans was 1215 miles long 176 years ago.It was 1180 miles after the cut-off of 1722..its length is only 973 miles at present (1875).Any calm person who is not blind or idiotic can see that 710 years from now the lower Mississippi will only be about 2 miles long.

1.Graph the points given and calculate the linear regression equation for these data.

2.Whats wrong with the reasoning?

Although the three points may seem to lie along a straight line, the graph must actually curve later on. The river cannot become any shorter after all the bends are gone

3.Give an example of a similar jump to conclusions.

4.The table represents the average blue book value for a Honda Civic LX bought in 2003 for $15,000.The number zero represents the purchase year (2003) and the numbers 1 6 represent the years since purchase.

Year

0

1

2

3

4

5

6

Value

$15,000

$13,200

$12,075

$11,050

$9500

$7900

$7100

1. Make a scatter plot of you data as a check for linearity and outliers.

1. Guess a reasonable correlation coefficient for your scatter plot.

1. Find the equation of the regression line for your data.

1. What is the correlation coefficient determined by your calculator?

1. Use your regression line to predict the value of the car in 2012 (remember, year 0 is 2003).Is this a reasonable prediction?Why or why not?

5.Plot the points given on a scatter plot.

x

1

1

2

2.5

3

3.5

4

4

4.5

5

5

5.5

2

y

1

2

1.5

2.5

3

3

3.5

4

4

5

6

6

6

a.Calculate the regression line for the data and sketch it on the plot.

b.An outlier on a scatter plot is an observation that is far from the regression line so it produces a large residual.Label the outlier for this graph Point A.

c.Calculate the regression line for the data without Point A and sketch it on the plot in a different color.

d.Comment on the effect Point A has on the regression line for the data.

6.Consider this new set of data and accompanying scatter plot.

x

1

1.5

2

2

2.5

2.5

3

3

3

3.5

4

7

y

3

2

3

4

1

2

1

2

3

2

1

7

8

7

6

5

4

3

2

1

0

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1. Draw a line where you predict the regression line for this set of points will lie.

1. Identify the potential outlier for this data as Point B.

1. Calculate and graph the regression lines for the data points with and without Point B.

1. Comment on the difference in the two lines.

1. Both Point A and Point B are considered outliers for their data sets.Which would you classify as an influential point?