Questions 1 through 6 work with the length of the sidereal year vs. distance from the sun. The table of data is shown below.

1.Draw a scatter plot of Distance vs. Year (using the untransformed data) with the least squares regression line. Does the line seem to model the relationship well?

2.On your calculator do a linear regression (STAT, CALC 8) for these different combinations:

Distance vs. In(Year) (L1 vs. L4 if you entered the data as directed above)

Ln(Distance) vs. Year (L3 vs. L2 if you entered the data as directed above)

Ln(Distance) vs. Ln(Year) (L3 vs L4 if you entered the data as directed above)

Which transformation yields the highest correlation coefficient (Pearson's r)? Sketch a scatter plot of this transformation and show the least squares line. What's the values of r and r2 for that transformation and what regression equation does it yield?

3.Using the regression equation from the previous question that best fits the data, place the values of the residuals into L5. Create a residual plot on your calculator and interpret it, you don't need to draw the plot.

4.Using algebra convert your regression equation to a power equation (Show your work below). Enter this equation in Y2 and make a scatter plot of L1, L2, with Y2, verifying that the power equation is a good fit for this data.

As you set up your regression equation keep in mind that the variables are Inyhat and Inx.

Here's what the graph of the scatter plot and power equation will look like

\fIncrease in Life Expectancy in the United States during the 20th Century Expected Expected Year Life Span Year Life Span 1920 54.1 1975 72.6 1930 59.7 1980 73.7 1940 62.9 1985 74.7 1950 68.2 1990 75.4 1960 69.7 1995 75.8 1970 70.8 Source: National Center for Health Statistics, published in the 1998 World AlmanacYear Medicare Expenditures (billions of dollars 1970 7.6 1980 37.5 1985 72.1 1990 112.1 1991 124.4 1992 141.4 1993 153 1994 169.8 1995 187.9 1996 203.1