2. (35 pts) An article in Optical Engineering, "Operating curve extraction of a correlator's filter" (2004, Vol. 43, pp. 2775-2779) reported on use of an optical correlator to perform an experiment by varying brightness (xi) and contrast (x2). The resulting modulation is characterized by the useful range (y) of gray levels. The data are shown below. Brightness (%): 54 61 65 100 100 100 50 57 54 Contrast (%): 56 80 70, 50 65 80 25 35 26 Useful range (ng): 96 50 50 112 96 80 155 144 255 (a) (15 pts) Using R/RStudio, fit a multiple linear regression model to these data. Round your answers to 4 decimal places. Also, show your R code here with the result summary. B = ( ), B =( ), B=( ) I*