Question

Because the universe is expanding, objects in space are constantly moving apart. This can be confirmed by the appearance of redshift; things moving away from us look redder, and things moving towards us look bluer. The further an object is from us, the more of an effect this redshift has. The table below lists the measured amount of redshift of six galaxies, along with how far those galaxies are from Earth (in billions of light years). Distance 0.32 0.75 1.00 0.55 0.61 0.14 Redshift 0.0233 0.0539 0.0718 0.0395 0.0438 0.0103 (A) Using your calculator, find a line of best fit for this equation. List the equation for the line, along with the coefficient of correlation and p-value. Round your values to four decimal places.

(B) Explain whether or not you feel we have enough evidence to deduce that there is a linear correlation between redshift and distance.

(C) Using your line of best fit, how much redshift would you predict for a galaxy that was 2 billion light years away? Round your answer to four decimal places.

(D) If you discovered a new galaxy with a redshift of 0.03, how far away would you predict that it is? Use your line of best fit, and round your answer to two decimal places

Answer 1

A) Regression equation :

Redshift = 0.0003146 + 0.07143 * Distance

Coefficient of correlation = 1.0000

P avlue = 9.3E-11

B) There is a perfectly positive linear correlation between redshift and distance.

C) Distance = 2 billion,

Redshift = 0.0003146 + 0.07143 * 2 = 0.1432

D) Redshift = 0.03,

Distance = ( 0.03 - 0.0003146 ) / 0.07143 = 0.42 PL??