Final answer:
To find the regression equation, use the method of least squares. For part b, plug the desired price into the equation and solve for the year.
Step-by-step explanation:
To find the regression equation for the given table, we need to use the method of least squares. The regression equation is in the form of y = mx + b, where y is the dependent variable (in this case, the average price of a movie ticket), x is the independent variable (in this case, the year), m is the slope of the line, and b is the y-intercept.
To find the slope, we use the formula:
m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2),
where n is the number of data points, Σ represents the sum, x and y are the values from the table. To find the y-intercept, b, we can use the formula:
b = (Σy - mΣx) / n.
By substituting the values from the table into the formulas, we can find the regression equation. For part b, we can plug the desired price of $157 into the regression equation and solve for the year.