In: Statistics and Probability
Use simple regression to see if there is any significant change in real profits over time.
use the following data.
Bob's Real Profit |
$40,977.46 |
$43,055.59 |
$35,652.90 |
$33,888.98 |
$38,100.50 |
$39,346.52 |
$30,587.85 |
$28,261.74 |
$31,394.09 |
$33,218.12 |
$37,989.71 |
$37,899.32 |
$42,310.40 |
$43,916.94 |
$36,274.07 |
$34,235.34 |
$37,594.17 |
$38,457.01 |
$30,010.49 |
$27,735.00 |
$32,423.16 |
$33,171.59 |
$36,624.22 |
$36,424.14 |
$40,765.89 |
$42,595.34 |
$34,941.99 |
$33,042.55 |
$37,539.56 |
$38,741.28 |
$30,312.99 |
$27,232.19 |
$31,716.82 |
$32,556.00 |
$36,628.84 |
$36,453.94 |
$40,985.92 |
$43,020.60 |
$35,538.57 |
$33,314.94 |
$37,376.67 |
$38,766.05 |
$30,280.77 |
$27,515.09 |
$32,801.94 |
$33,179.84 |
$36,784.42 |
$38,279.24 |
$42,610.51 |
$44,031.32 |
$35,092.19 |
$32,991.10 |
$37,338.19 |
$38,174.58 |
$30,169.31 |
$27,736.26 |
$30,938.52 |
$31,480.40 |
$35,317.94 |
$34,850.41 |
$40,093.80 |
$43,590.19 |
$36,638.51 |
$34,307.72 |
$38,165.20 |
$39,666.29 |
$29,945.27 |
$26,785.90 |
$31,463.88 |
$31,198.36 |
$34,628.97 |
$35,469.75 |
$40,984.54 |
$42,230.32 |
$34,786.05 |
$33,010.05 |
$37,466.74 |
$38,555.37 |
$29,930.83 |
$27,120.02 |
$31,336.66 |
$31,161.55 |
$35,229.86 |
$35,825.63 |
$40,117.09 |
$42,191.40 |
$35,381.10 |
$32,609.91 |
$36,294.82 |
$37,742.67 |
$29,391.27 |
$26,428.62 |
$30,914.48 |
$31,198.30 |
$35,395.77 |
$36,063.68 |
$40,815.77 |
$42,232.40 |
$33,833.75 |
$32,214.95 |
$36,351.62 |
$38,132.14 |
$29,251.63 |
$27,579.49 |
$31,099.74 |
$32,846.78 |
$36,648.48 |
$35,950.59 |
$35,193.79 |
To test whether the real profit of Bob changes significantly over time, a simple linear regression model is fitted over time. If the regression coefficient slope is significant then we can consider that the real profit change over time.
The slope of the regression line is -21.05. Which means that the average real profit of Bob decreases by $21.05 per month. But this regression coefficient is not significant.