Question

Find the value of the coefficient of determination.

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line. bo + bjt, for predicting the number of bids an item will receive based on the list price. Keep in mind. the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 21 37 40 41 44 10 Number of Bids | 2 | 5 6 | io! Table Copy Data Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places. Tables Keypad How to enter your answer Previous step answers

Answer 1

$Since~the~value~corresponding~to~41~is~not~visible~so~we~ignore~this~pair\\ for~computation~and~compute~coefficient~of~determination~using~remaining\\ 4~pairs~i.e.~(x,y):~(21,2),(37,5),(40,6),(44,10).\\ where,~x=price~in~dollars,~y=number~of~bids\\ \bar{x}=(21+37+40+44)/4= 35.5,~\bar{y}=(2+5+6+10)/4=5.75,\\ \sum_{i=1}^4x_i^2=21^2+37^2+40^2+44^2=5346,~\sum_{i=1}^4y_i^2=2^2+5^2+6^2+10^2=165,\\$

$\sum_{i=1}^4x_iy_i=21*2+37*5+40*6+44*10=907,~S_{xx}=\sum_{i=1}^4x_i^2-4\bar{x}^2=305, \\S_{yy}=\sum_{i=1}^4y_i^2-4\bar{y}^2=32.75 ,~S_{xy}=\sum_{i=1}^4x_iy_i-4\bar{x}\bar{y}=90.5.\\ Coefficient~of~determination=r^2=\frac{S_{xy}^2}{S_{xx}S_{yy}}=0.820.$