Question

Can someone help me with this question, I do not know how to do the long-distance in excel.

If you could show me the Excel data as well that would be great.

retention 10.18 The following are the average distances of the planets in the solar system from the 25 Distance (millions of miles) 47.163 67.235 92.960 141.61 313.00 483.60 886.70 1783.0 2794.0 3666.0 Planet No. Planet Mercury Venus Earth Mars Asteroids Jupiter Saturn Uranus Neptune Pluto 4 10 (a) How does the distance of a planet from the sun increase with the planet number? Find a transformation of the distance that gives a linear relationship with respect to the planet number. (b) Fit a least squares straight line after linearizing the relationship. (c) It is speculated that there is a planet beyond Pluto, called Planet X. Predict its distance from the sun.

Answer 1

Hello,
Here the planet number is the depend on the distance.
we fit the linear regression model.

Y=a+bx+e

Where y- dependent variable

X-independent variable

A-intercept

b – Regression coefficient

E-random error

Input data in theExcel,
follow the path
data>datat analysis >regression
the excel output of the above regression is

Regression Statistics
Multiple R	0.887914
R Square	0.788392
Adjusted R Square	0.761941
Standard Error	630.3226
Observations	10

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1056.24	430.5923	-2.45299	0.039751	-2049.19	-63.2909	-2049.19	-63.2909
planet no	378.8664	69.39623	5.459467	0.000602	218.8384	538.8944	218.8384	538.8944

Here planet number is significant and r-square is 0.78.

PREDICTION OF y,

The estimated regression equation as,
y=-1056.24+378.86X   ……………estimated regression equation
if the x=x then regression equation as

y=-1056.24+378.86X   , after substituting the value of the x we can get the distance.
thanks