2.a) The average participation rate is 87.36% and the average match rate is $0.732, meaning the firm match 73.2 cents per contributed dollar, in the sample of 401k plans.
b) The simple linear regression function is Participation Rate = beta0 + beta1*(Match Rate). It is calculated to be Participation Rate = 83.08 + 5.86*(Match Rate). This function reveals as the firm increases Match Rate, Participation Rate will increase.
c) The y-intercept for the function is 83.08, meaning this is employee participation in the program
d) The coefficient, or the slope of the function, on match rate is 5.86. For every additional unit of Match Rate the firm increase, the participation will increase 5.86 units.
e) Participation Rate = 83.08 + (3.5*5.86) = 103.58
This is not a reasonable expectation because participation cannot be above 100%, and the solution is greater. The linear function minimizes error on the low end of the regression line. Since 3.5 is on the high end of the regression line, there will be a higher error.
f) The R-square value is .0747. This value, in my opinion, is not high. Since it is low, one can expect Participation Rate and Match Rate to not be very related.
3.a) The regression function is as follows:
Birth Weight = 119.77 - .51*(Cigarettes Smoked)
On average, for every Cigarette Smoked by the mother, the Birth Weight of the child will decrease by .051 ounces.
b) The correlation coefficient is 0.15. With little correlation, one can assume that there are many other factors besides the number of cigarettes smoked that will affect birth rate.
c) Birth Weight = 119.77 - .51*(Cigarettes Smoked) rearranged to sol ...