Many of today’s leading companies, including Google, Microsoft, and Facebook, ar

Question

Many of today’s leading companies, including Google, Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who would like to analyze university factors that enhance innovation. She collects data on 143 universities in 2008 for a regression where the response variable is the number of startups (Startups), which is used as a measure for innovation. The explanatory variables include the university’s research expenditure in millions of dollars (Research), the number of patents issued (Patents), and the age of its technology transfer office in years (Duration).

A) output for A

B) output for B

a) Develop a simple linear equation to predict number of startups based on research.

Perform the test of significance on the slope of this equation using alpha = .05. Be sure to show all necessary parts of the hypothesis test.

b) Develop a simple linear equation to predict number of startups based on duration.

Perform the test of significance on the slope of this equation using alpha = .05. Be sure to show all necessary parts of the hypothesis test.

c) Compute the coefficient of determination for the regression using research to predict the number of startups. Interpret the coefficient of determination.

d) Compute the coefficient of determination for the regression using duration to predict the number of startups. Interpret the coefficient of determination.

e) Which regression equation provides a better prediction of startups? Support your answer with the diagnostics provided in parts a - d above.

Name of Institution Startups Research Patents Duration Albert Einstein College of Med/Yeshiva Univ. 1 145.5236 8 23 Arizona State Univ. 1 237.5212 16 23 Auburn Univ. 1 146.9840 12 20 Baylor College of Medicine 1 304.2250 11 25 Boston Univ./Boston Medical Ctr. 12 343.4238 9 32 Bowling Green State Univ. 0 10.7120 0 7 Brigham Young Univ. 9 26.3600 3 22 Calpoly State Univ, SLO 0 14.8700 0 8 Carnegie Mellon Univ. 10 229.2800 21 16 Clemnson Univ. 3 139.2837 15 21 Colorado State Univ. 3 302.6129 9 38 Columbia Univ. 10 640.0000 59 26 Cornell Research Fdn., Inc. 5 668.2275 54 29 Dartmouth College 1 174.1091 13 23 Drexel Univ. 4 102.2090 8 13 Duke Univ. 7 678.1842 32 22 Duquesne Univ. 0 13.2000 1 9 East Carolina Univ. 1 16.1920 4 13 Eastern Virginia Medical School 0 30.7770 3 9 Emory Univ. 3 390.9652 3 23 Florida Atlantic Univ. 0 43.2491 2 12 Florida State Univ. 3 206.5418 11 12 George Mason Univ. 5 79.8832 5 12 Georgetown Univ. 0 144.9570 12 15 Georgia Inst. Of Technology 9 536.4125 46 18 Harvard univ. 12 660.0815 55 31 Indiana Univ. (ARTI) 2 404.6215 8 17 Iowa State Univ. 2 251.6740 27 73 Johns Hopkins Univ. 12 1183.7680 45 35 Johns Hopkins Univ. Applied Physics Laboratory 1 819.2889 23 9 Kansas State Univ. Research Fdn. 3 95.8786 5 66 Kent State Univ. 0 18.4444 8 19 Louisiana State Univ. System 2 391.7670 25 22 Louisiana Tech Univ. 1 19.4060 6 8 Massachusetts Inst. Of Technology (MIT) 20 1319.0000 140 68 Medical College of Georgia Research Inst. 0 57.0852 1 7 Medical College of Wisconsin Research Fndtn 1 134.2000 4 24 Medical Univ. of South Carolina 2 161.1623 0 14 Michigan State Univ. 3 356.7670 48 16 Michigan Technological Univ. 2 60.3560 8 20 Mississippi State Univ. 4 210.9510 7 13 Montana State Univ. 2 96.1506 9 28 Mount Sinai School of Medicine of NYU 0 296.3800 13 17 New Jersey Inst. Of Technology 0 89.7920 11 18 New Mexico State Univ. 0 120.3234 1 18 New York Univ. 6 310.6990 30 19 North Carolina State Univ. 5 366.1370 37 24 North Dakota State Univ. 0 115.5130 9 13 Northeastern Univ. 2 56.7275 3 8 Ohio State Univ. 5 702.5635 15 18 Ohio Univ. 3 25.9776 5 17 Oklahoma State Univ. 2 138.7592 4 13 Oregona Health & Science Univ. 4 279.8494 13 19 Oregon State Univ. 1 188.0560 11 28 Penn State Univ. 1 717.2440 38 19 Portland State Univ. 0 40.1469 2 3 Purdue Research Fdn. 11 495.0990 24 20 Rensselaer Polytechnic Inst. 1 63.1974 20 15 Research Foundation of SUNY 10 784.3243 44 29 Rice Univ. 2 83.5624 34 10 Rutgers, The State Univ. of NJ 2 323.4040 36 19 San Diego State Univ. 0 106.8504 1 11 Stanford Univ. 9 694.2175 132 38 Stevens Inst. Of Technology 2 29.1348 3 8 Temple Univ. 0 150.3760 4 19 Texas A&M Univ. System 1 582.3650 28 16 The UAB Research Fdn. 1 404.6150 10 21 Thomas Jefferson Univ. 0 94.0318 5 24 Tufts Univ. 2 151.0077 8 30 Tulane Univ. 1 146.8751 5 23 Univ. of Akron 5 49.5978 4 13 Univ. of Alabama 3 32.8460 4 2 Univ. of Alabama in Huntsville 10 65.3200 1 9 Univ. of Arizona 6 547.1974 19 20 Univ. of Arkansas for Medical Sciences 0 115.5379 10 14 Univ. of Arkansas, Fayetteville 1 110.8750 4 18 Univ. of California System 55 4403.6620 224 29 Univ. of Central Florida 2 108.0000 57 23 Univ. of Chicago/UC Tech 0 317.5155 29 22 Univ. of Cincinnati 0 211.3931 8 25 Univ. of Colorado 11 661.0000 28 15 Univ. of Connecticut 3 161.3362 23 21 Univ. of Delaware 0 166.3700 12 11 Univ. of Florida 14 483.7980 52 25 Univ. of Georgia 2 350.2990 33 29 Univ. of Hawaii 0 211.7782 11 21 Univ. of Houston 1 84.4900 5 12 Univ. of Idaho 0 81.5322 2 22 Univ. of Illinois, Chicago, Urbana 11 830.7790 55 27 Univ. of Iowa Research Fdn. 0 293.5640 24 33 Univ. of Kansas 2 197.7970 4 14 Univ. of Kentucky Research Fdn. 8 242.9660 15 24 Univ. of Louisville 3 164.1230 6 12 Univ. of Maryland Biotechnology Inst. 0 43.2130 7 8 Univ. of Maryland, Baltimore 2 377.4180 13 19 Univ. of Maryland, Baltimore Country 0 66.8014 9 14 Univ. of Maryland, College Park 3 346.3693 23 21 Univ. of Massachusetts 2 435.2470 25 14 Univ. of Miami 0 325.3000 4 19 Univ. Of Michigan 13 875.7535 75 26 Univ. Of Minnesota 1 583.5240 37 51 Univ. of Mississippi 3 54.7090 6 16 Univ. of Missouri, all campuses 6 354.7636 20 21 Univ. of Nebraska 3 342.6482 13 16 Univ. of New Hampshire 0 98.8208 5 11 Univ. of New Mexico/Sci. & Tech. Corp. 6 197.6285 11 13 Univ. of North Carolina at Greensboro 2 33.1258 2 6 Univ. of North Carolina, Chapel Hill 5 619.6000 17 23 Univ. of North Carolina, Charlotte 3 29.8081 6 15 Univ. of North Texas Health Science Ctr. 0 31.8954 2 9 Univ. of Notre Dame 0 103.3000 4 9 Univ. of Oklahoma, All Campuses 1 158.9638 18 24 Univ. of Oregon 0 101.3423 4 16 Univ. of Pennsylvania 2 667.3547 44 22 Univ. of Pittsburgh 3 641.6260 36 16 Univ. of Rochester 6 361.6022 25 28 Univ. of South Alabama 0 28.0793 2 13 Univ. of South Carolina 5 185.1979 5 15 Univ. of South Dakota 0 22.7420 0 2 Univ. of South Florida 5 298.5000 31 18 Univ. of Southern California 5 484.6000 41 37 Univ. of Tennessee 2 246.3971 15 25 Univ. of Texas at Austin 10 527.1413 25 17 Univ. of Texas Health Science Ctr., Houston 2 197.2517 3 23 Univ. of Texas Health Science Ctr., San Antonio 0 201.3230 6 18 Univ. of Texas Medical Branch 2 153.4613 10 20 Univ. of Texas Southwestern Med. Ctr. 2 377.1696 15 18 Univ. of Texas, Arlington 2 66.6105 8 9 Univ. of Toledo 3 59.5830 5 14 Univ. of Utah 20 273.0059 33 40 Univ. of Vermont 5 90.6422 5 10 Univ. of Virginia Patent Fdn. 2 257.6510 12 31 Univ. of Washington/Wash. Res. Fdn. 9 1026.7885 56 25 Univ. of West Florida 0 14.4730 0 1 Utah State Univ. 0 148.2570 6 21 Vanderbilt Univ. 4 444.3325 16 18 Virginia Commonwealth Univ. 3 148.6550 6 14 Virginia Tech Intellectual Properties, Inc. 3 199.6359 23 23 W.A.R.F./Univ. of Wisconsin Madison 6 942.0000 98 83 Wake Forest Univ. 2 148.6864 10 23 Washington State Univ. Research Fdn. 2 140.8622 6 69 Wayne State Univ. 1 249.2100 7 20 West Virginia Univ. 1 154.3820 3 9 SUMMARY OUTPUT Regression Statistics Multiple R 0.838425654 0.702957578 R Square Adjusted R Square 0.700850894 Standard Error 3.189941213 143 Observations 1 3395.432574 3395.4326 33 3.6796733 5.43907 E-39 Regression Residual 141 1434.777216 10.175725 Total 142 4830 20979 P-value Coefficients Standard Error t Stat Lower 95% Upper 95% Lower 95.0% LUpper 95.0% 0.21478072 0.326612478 0.6576011 os11866598 .0.43090977 0.86047121 -0.430909773 0.860471214 intercept 0.011381616 0.000623073 18.266901 5.43907 E-39 0.010149843 0.01261339 0.010149843 0.012613389

Explanation / Answer

Part-a The simple linear equation to predict number of startups based on research is

Startups=0.2148 + 0.0114 Research

We have to test the null hypothesis H0:=0 versus alternative Ha:0

From regression results test statistic is t=18.27 with p-value=5.44E-39

=0.000.

We choose alpha=0.05 as out level of significance.

P-value of test of significance of slope is p=5.44E-39 which is less than 0.05, so we reject the null hypothesis and conclude that research is significant in explaining the startup and corresponding to 1 million dollar increase in research there is on an average an increase of 0.0114 in startups.

Part-b The simple linear equation to predict number of startups based on duration is

Startups=1.0674 + 0.1263 Duration

We have to test the null hypothesis H0:=0 versus alternative Ha:0

From regression results test statistic is t=3.40 with p-value=0.0009

We choose alpha=0.05 as out level of significance.

P-value of test of significance of slope is p=0.0009 which is less than 0.05, so we reject the null hypothesis and conclude that duration is significant in explaining the startup and corresponding to 1 year increase in technology transfer there is on an average an increase of 0.1263 in startups.

Part-c

The coefficient of determination for research is R2=0.7030 which means that research explained 70.30% variability in startup.

Part-d

The coefficient of determination for duration is R2=0.0758 which means that duration explained 7.58% variability in startup.

Part-e

The regression of startup on research provided a better prediction of startup as it has very high R-square as compared to duration.

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