Question

3-part question based on this data:

Planet	Distance from Sun (in millions of miles)	Years (as a fraction of Earth years)	ln(Dist)	ln(Year)
Mercury	36.19	0.2410	3.5889	-1.4229
Venus	67.63	0.6156	4.2140	-0.4851
Earth	93.50	1.0007	4.5380	0.0007
Mars	142.46	1.8821	4.9591	0.6324
Jupiter	486.46	11.8704	6.1871	2.4741
Saturn	893.38	29.4580	6.7950	3.3830
Uranus	1,794.37	84.0100	7.4924	4.4309
Neptune	2,815.19	164.7800	7.9428	5.1046
Pluto	3,695.95	248.5400	8.2150	5.5156

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

b) Do a linear regression for Distance vs. ln(Year), Ln(Distance) vs. Year, Ln(Distance) vs. Ln(Year)

c) Which transformation yields the highest correlation coefficient (Pearson's r)? Sketch a scatterplot of this transformation and show the least-squares line. What is the value of r and r² for that transformation, and what regression equation does it yield?

Answer 1

a)

There seems to be a linear relationship between Distance and Year.

b)

It is being performed on Excel by using the function LINEST, it can be executed by selecting 2 columns and 5 rows and then type in the first row and first column cell =LINEST(y_values,x_values, TRUE, TRUE) and then press shift+ctrl+enter.

c)

The highest correlation coefficient is in the third case of 0.99, which is Ln(distance) vs Ln(Year)

This is the scatterplot for Ln(distance) vs Ln(Year)