For all the restaurants in a city, the prediction equation for \(y=\) average monthly visitor satisfaction rating (range \(0-4.0\) where \(0=\) very poor and \(4=\) very good) and \(x_{1}=\) the monthly food quality score given by the food inspection authority (range \(0-4.0\) where \(0=\) very poor and \(4=\) very good) and \(x_{2}=\) the number of visitors in a month is \(\hat{y}=0.35+0.55 x_{1}+0.0015 x_{2}\).

a. Find the predicted average monthly visitor satisfaction rating for a restaurant having (i) a monthly food quality score of 4.0 and 800 visitors in a month and (ii) a monthly food quality score of 2.0 and 200 visitors in a month.

b. For restaurants with \(x_{2}=500\), show that \(\hat{y}=1.10+0.55 x_{1}\).

c. For restaurants with \(x_{2}=600\), show that \(\hat{y}=1.25+0.55 x_{1}\). Thus, compared to part \(\mathrm{b}\), the slope for \(x_{1}\) is still 0.55 , and increasing \(x_{2}\) by 100 (from 500 to 600) shifts the intercept upward by \(100 \times\left(\right.\) slope for \(x_{2}\) ) \(=100(0.0015)=0.15\) units.