In the United States, the revenue (money taken from sales) at a "full service" restaurant is increasing at a faster rate than the revenue at a "fast food" restaurant. The data below represent the annual revenue in billions of dollars for each type of restaurant. Use the data to answer the three questions below. Let x=0 represent the year 1990. Year 1995 1999 2000 2001 2002 2003 2004 Full Service 82 111 124 131 139 146 156 Fast Food 107 111 113 118 120 124 127 Question content area bottom Part 1 a) Write a linear regression equation for the "full service" restaurant. y=8.229 x plus 40.0118.229x+40.011 (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) Part 2 b) Now write a linear regression equation for the "fast food" restaurant. y=enter your response here (Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.)

Question

In the United​ States, the revenue​ (money taken from​ sales) at a​ "full service" restaurant is increasing at a faster rate than the revenue at a​ "fast food" restaurant. The data below represent the annual revenue in billions of dollars for each type of restaurant. Use the data to answer the three questions below. Let x=0 represent the year 1990. Year 1995 1999 2000 2001 2002 2003 2004 Full Service 82 111 124 131 139 146 156 Fast Food 107 111 113 118 120 124 127 Question content area bottom Part 1 ​a) Write a linear regression equation for the​ "full service" restaurant. y=8.229 x plus 40.0118.229x+40.011 ​(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as​ needed.) Part 2 ​b) Now write a linear regression equation for the​ "fast food" restaurant. y=enter your response here ​(Type an expression using x as the variable. Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as​ needed.)

Bot GPT 3.5 · Answer

Part 1: To find the linear regression equation for the "full service" restaurant, we can use the given data points: (0, 82), (5, 111), (9, 124), (10, 131), (11, 139), (12, 146), (13, 156). Using these points, we can calculate the slope (m) and y-intercept (b) using the formula: y = mx + b. First, calculate the slope: m = (y2 - y1) / (x2 - x1) m = (111 - 82) / (5 - 0) m = 29 / 5 = 5.8 Next, substitute one of the given points and the calculated slope into the formula to find the y-intercept: 82 = 5.8(0) + b b = 82 Therefore, the linear regression equation for the "full service" restaurant is: y = 5.8x + 82 Part 2: To find the linear regression equation for the "fast food" restaurant, we can use the given data points: (0, 107), (5, 111), (9, 113), (10, 118), (11, 120), (12, 124), (13, 127). Using these points, we can calculate the slope (m) and y-intercept (b) using the formula: y = mx + b. First, calculate the slope: m = (y2 - y1) / (x2 - x1) m = (111 - 107) / (5 - 0) m = 4 / 5 = 0.8 Next, substitute one of the given points and the calculated slope into the formula to find the y-intercept: 107 = 0.8(0) + b b = 107 Therefore, the linear regression equation for the "fast food" restaurant is: y = 0.8x + 107