Question

In: Statistics and Probability

15.30 Note: This exercise requires a computer and statistical software. The data mentioned below can be...

15.30 Note: This exercise requires a computer and statistical software. The data mentioned below can be found in several formats on your Premium Website under "Chapter datasets".

For the top law firms in the world in terms of profit per equity partner, data file XR15012 lists the number of equity partners and the gross revenue ($ millions) for the most recent fiscal year. Given these data, determine the least-squares equation for predicting gross revenue on the basis of the number of equity partners, then interpret its slope. (SOURCE: law.com, August 8, 2009.)

Please round your answers to 1 decimal place.

a. The point estimate for gross revenue when there are 200 equity partners is $ million

b. For an individual law firm having 200 equity partners, the lower bound of the 90% prediction interval for gross revenue is $ million

c. For an individual law firm having 200 equity partners, the upper bound of the 90% prediction interval for gross revenue is $ million

c. For all law firms having 200 equity partners, the lower bound of the 90% confidence interval for their mean gross revenue is $ million.

d. For all law firms having 200 equity partners, the upper bound of the 90% confidence interval for their mean gross revenue is $ million.

partners gross_revenue
76 578.5
90 610.5
167 985.0
126 839.0
79 384.5
401 2358.5
109 966.0
76 587.0
111 651.0
440 2588.5
112 642.5
220 1310.0
79 419.5
163 836.5
395 2660.5
159 478.0
137 709.5
421 2170.0
445 2005.5
363 2034.5
133 603.0
189 894.0
192 1175.0
131 646.5
142 844.5
194 975.0
265 907.5
183 921.0
287 1373.0
144 772.0
224 934.0
92 430.5
142 537.5
125 577.5
85 431.0
156 628.0
174 611.0
281 978.0
136 464.0
187 1074.0
119 531.0
251 1033.0
129 485.0
134 615.5
332 1386.0
139 743.5
254 733.0
231 959.0
124 470.5
288 1200.0
200 577.5
144 579.0
185 697.5
242 894.5
158 594.5
83 372.5
318 1183.0
276 1134.5
199 752.5
711 2188.0
99 367.5
235 596.0
296 880.0
107 391.0
178 467.0
187 457.0
144 461.0
145 781.0
320 944.0
85 354.5
148 518.0
138 491.0
137 475.0
268 892.0
109 462.5
174 590.0
92 329.0
238 720.5
130 478.0
211 508.0
248 653.5
155 530.5
123 375.0
243 755.0
510 1441.0
356 649.5
159 394.5
147 263.5
169 412.0
196 612.5
215 442.5
176 469.0
192 367.0
174 349.0
211 456.5
84 228.0
203 357.0
146 315.0
64 193.5
248 305.0

Solutions

Expert Solution

the leaset square regression line is given as

gross_revenue(y)=a+b*partners(x)=27.99+3.81*x

(a) for x=200, y=27.99+3.81*200=789.99

(b)

(1-alpha)100% prediction interval of y^(for given x)=y^ t(alpha/2,error df)*Se*sqrt(1+1/n+(x-x- )2/Sxx)

90% prediction interval=

=789.991.66*301.83*sqrt(1+1/100+(200-196.08)*(200-196.08)/1097245)=789.99503.54

=(286.45, 1293.53)

(c) (1-alpha)100%confidence interval of y^(for given x)=y^ t(alpha/2,error df)*Se*sqrt(1/n+(x- )2/Sxx)

90%confidence interval=

=789.991.66*301.83*sqrt(1/100+(200-196.08)*(200-196.08)/1097245)=789.9950.14=(739.49,740.13

following regression analysis information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.80030665
R Square 0.640490734
Adjusted R Square 0.636822272
Standard Error 301.8331351
Observations 100
ANOVA
df SS MS F Significance F
Regression 1 15906061.89 15906062 174.5938 1.7E-23
Residual 98 8928117.661 91103.24
Total 99 24834179.55
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 27.98837174 64.05685582 0.43693 0.663123 -99.1304 155.1071
X Variable 1 3.807408345 0.288147621 13.2134 1.7E-23 3.235589 4.379228

orchestra answered 2 years ago
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