Consider the following data points: (36, 88), (67.25, 224.7), (93, 365.3), (141.

Question

Consider the following data points: (36, 88), (67.25, 224.7), (93, 365.3), (141.75, 687), and (483.8, 4332.1). (This was the data Kepler had when he was trying to find a relationship between the distance, in millions of miles, of a planet from the sun and the time, in days, it takes for that planet to go once around the sun.) Rather than fit a line y = b + mx to these data points (xi , yi), fit a line to the points (log xi , log yi). Use your fitted line to guess a simple relationship between x and y. (In many applications to science and social science, data is transformed before regression is employed. The most commonly used transformations are power transformations and logarithmic transformations.)

Explanation / Answer

here we fit regression by using excel then we get above output

by using this output we can say that there is linear realtion ship between log x and logy

here coefficent of determination ie R^2=1 therefore we conclude that 100% variation in logy is explainedd by the linear relationship with log x

Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 1 Standard Error 0.00012 Observations 5 ANOVA df SS MS F Significance F Regression 1 1.601595 1.601595 1.1E+08 1.9E-12 Residual 3 4.35E-08 1.45E-08 Total 4 1.601595 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.3894 0.000296 -1317 9.65E-10 -0.39034 -0.38845 -0.39034 -0.38845 X Variable 1 1.499643 0.000143 10511.23 1.9E-12 1.499189 1.500097 1.499189 1.500097

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