In 1988, only 24% of primary care doctors in the UK were women. Since that time, the percentage of female...

5. In 1988, only 24% of primary care doctors in the UK were women. Since that time, the percentage of female primary care doctors has consistently been increasing. The function F represents the percent of primary care doctors that were women in a given year, where t = 0 represents the year 1988. The table above gives values for F at selected values of t.
The function F can be modeled by the linear regression function y = at + b, where a and b are constants.
a) Based on the data presented in the table, explain why a linear regression model for F is appropriate.
b) Find the equation of the linear regression model y = at + b.
c) Using the model found in part b, what is the predicted percentage of female primary care doctors in the UK for the year 2021 (t = 33)?
d) In 2021, the women accounted for 55% of all primary care doctors in the UK. What is the residual for this value?