(30 pts)
The effect of sealer plate temperature and sealer plate 
clearance in a soap wrapping machine affects the percentage
of wrapped bars that pass inspection. Some data on these
variables were collected and are shown as follows:

Plate Clearance, X1 Plate Temperature, X2 %Sealed Properly, Y
130 190 35.0
174 176 81.7
134 205 42.5
191 210 98.3
165 230 52.7
194 192 82.0
143 220 34.5
186 235 95.4
139 240 56.7
188 230 84.4
175 200 94.3
156 218 44.3
190 220 83.3
178 210 91.4
132 208 43.5
148 225 51.7

Assume the standard linear model, Y = B0 + B1X1 + B2X2 + e.
a) Find the OLS estimates of the betas.
Provide standard errors and t-statistics for each of the coefficients.
b) Is the overall regression significant? Use alpha = 0.05.
How much of the variation in Y about Ybar is explained by X1 and X2?
c) Is one of the variables more useful than the other in predicting
the percentage sealed properly?
d) Give a 95% confidence interval for the mean % Sealed properly at a 
clearance of 180 and a temperature of 200. Give a 95% prediction
interval for the same situation. 
e) What recommendations would you make concerning the operation
of the wrapping machine?