Concept explainers
(a)
To graph: A
(a)
Explanation of Solution
Given: The data for the average debt, percentage of students who borrow, admittance rate, four-year graduation rate, in-state tuition after aid, out-of-state tuition after aid, average aid per student and the number of students per faculty member 40 colleges in US.
College | Admit | Yr4Grad | StudPerFac | InAfterAid | OutAfterAid | AvgAid | PercBorrow | AvgDebt |
The University of Arizona, Tucson | 75 | 34 | 20 | 9565 | 25775 | 9261 | 44 | 20074 |
Stony Brook University, State University of New York, Stony Brook | 41 | 43 | 19 | 11193 | 20643 | 7275 | 59 | 19807 |
University of Illinois at Springfield, Springfield | 59 | 50 | 14 | 11489 | 20639 | 8213 | 61 | 17335 |
State University of New York College at Oneonta, Oneonta | 41 | 48 | 17 | 12649 | 21699 | 5311 | 75 | 17564 |
Iowa State University of Science and Technology, Ames | 81 | 37 | 17 | 9738 | 21610 | 6413 | 69 | 30062 |
University of South Florida, Tampa | 45 | 24 | 28 | 10598 | 19788 | 5966 | 52 | 21679 |
University of New Hampshire, Durham | 73 | 61 | 18 | 21947 | 35267 | 3955 | 76 | 35671 |
University of North Florida, Jacksonville | 51 | 20 | 21 | 9171 | 21922 | 5789 | 39 | 15300 |
University of South Carolina, Columbia | 70 | 46 | 19 | 14117 | 30301 | 5027 | 49 | 21811 |
State University of New York College at Brockport, Brockport | 42 | 42 | 18 | 12888 | 21938 | 5140 | 80 | 25733 |
The University of North Carolina at Chapel Hill, Chapel Hill | 32 | 76 | 14 | 6548 | 26374 | 11080 | 31 | 16165 |
Towson University, Towson | 57 | 40 | 17 | 11627 | 23139 | 7601 | 56 | 19069 |
University of California, Santa Barbara, Santa Barbara | 46 | 64 | 17 | 12711 | 34521 | 15389 | 47 | 17596 |
St. Mary's College of Maryland, St. Mary's City | 65 | 74 | 12 | 17696 | 29773 | 8664 | 70 | 17505 |
University of Georgia, Athens | 59 | 54 | 19 | 10288 | 28498 | 8970 | 45 | 15938 |
Christopher Newport University, Newport News | 60 | 42 | 17 | 15725 | 24947 | 5087 | 51 | 21572 |
The Ohio State University, Columbus | 68 | 49 | 19 | 12680 | 27575 | 7789 | 59 | 22830 |
University of Delaware, Newark | 54 | 62 | 12 | 15728 | 31998 | 6734 | 44 | 17200 |
California State Polytechnic University, Pomona, Pomona | 45 | 20 | 26 | 10701 | 21861 | 8280 | 35 | 16704 |
University of Illinois at Urbana–Champaign, Champaign | 67 | 67 | 16 | 14809 | 28951 | 10885 | 51 | 21543 |
Auburn University, Auburn University | 79 | 36 | 18 | 13057 | 27649 | 6733 | 46 | 24777 |
The University of Alabama, Tuscaloosa | 54 | 38 | 19 | 11584 | 24884 | 6680 | 53 | 26701 |
University of Wisconsin–Madison, Madison | 58 | 51 | 17 | 12733 | 28483 | 5857 | 48 | 22837 |
The University of Texas at Dallas, Richardson | 50 | 42 | 19 | 14068 | 31094 | 6664 | 41 | 17384 |
State University of New York at Binghamton, Binghamton | 40 | 66 | 21 | 13310 | 21420 | 6716 | 50 | 21110 |
Rutgers, The State University of New Jersey, New Brunswick/Piscataway, Piscataway | 59 | 53 | 15 | 15629 | 28291 | 9937 | 68 | 16766 |
University of Science and Arts of Oklahoma, Chickasha | 56 | 18 | 14 | 4132 | 11092 | 7098 | 29 | 15339 |
Miami University, Oxford | 79 | 68 | 17 | 19310 | 34482 | 6083 | 51 | 27315 |
University of Maryland, College Park, College Park | 44 | 63 | 18 | 12450 | 29821 | 6959 | 43 | 22696 |
New College of Florida, Sarasota | 53 | 57 | 10 | 5316 | 28345 | 10142 | 36 | 11458 |
The University of North Carolina at Asheville, Asheville | 77 | 30 | 14 | 7443 | 21075 | 6202 | 48 | 15443 |
University of Mary Washington, Fredericksburg | 77 | 68 | 15 | 12206 | 23934 | 6500 | 57 | 15600 |
University of California, Los Angeles, Los Angeles | 23 | 68 | 17 | 15397 | 38275 | 12777 | 45 | 16733 |
University of Virginia, Charlottesville | 33 | 85 | 16 | 5138 | 29460 | 16488 | 32 | 19384 |
University of California, Berkeley, Berkeley | 22 | 69 | 17 | 13164 | 36042 | 15863 | 41 | 16056 |
University of Oklahoma, Norman | 85 | 33 | 18 | 11417 | 22370 | 6011 | 52 | 21517 |
The University of North Carolina at Wilmington, Wilmington | 57 | 45 | 17 | 7367 | 19188 | 6792 | 25 | 19277 |
University of Connecticut, Storrs | 54 | 66 | 18 | 14403 | 31299 | 8167 | 63 | 23237 |
University of Michigan, Ann Arbor | 51 | 72 | 15 | 13170 | 38842 | 10783 | 46 | 27828 |
University of Colorado at Boulder, Boulder | 83 | 41 | 18 | 14549 | 35727 | 7873 | 43 | 19758 |
Graph: To draw the scattered plot of each explanatory variable with AvgDebt of the provided data, below mentioned steps are followed in Minitab.
Step 1: Enter the data into Minitab worksheet.
Step 2: Go to Graph, select Matrix Plot, select Each Y versus each X and select Simple.
Step 3: Select AvgDebt as Y variable and Admit, Yr4Grad, StudPerFac, InAfterAid, OutAfterAid, AvgAid, PercBorrow.
Step 4: Press “OK”.
The obtained scattered plot is as follows:
Interpretation: The obtained scattered plot shows that the relationship between AvgDebt and AvgAid is negative linear while with all other variable it is positively linear.
(b)
To find: The Curves which fit the each of the predictors separately and to create a table which lists the explanatory variable, model standard deviation
(b)
Answer to Problem 14E
Solution: The table that shows the models for each explanatory variable, model standard deviation
Explanatory variable | Model | Model standard deviation s | P-value |
Admit, | |||
Yr4Grad | |||
StudPerFac | |||
InAfterAid | |||
OutAfterAid | |||
AvgAid | |||
PercBorrow |
Explanation of Solution
Given: The data for the average debt, percentage of students who borrow, admittance rate, four-year graduation rate, in-state tuition after aid, out-of-state tuition after aid, average aid per student and the number of students per faculty member 40 colleges in US.
College | Admit | Yr4Grad | StudPerFac | InAfterAid | OutAfterAid | AvgAid | PercBorrow | AvgDebt |
The University of Arizona, Tucson | 75 | 34 | 20 | 9565 | 25775 | 9261 | 44 | 20074 |
Stony Brook University, State University of New York, Stony Brook | 41 | 43 | 19 | 11193 | 20643 | 7275 | 59 | 19807 |
University of Illinois at Springfield, Springfield | 59 | 50 | 14 | 11489 | 20639 | 8213 | 61 | 17335 |
State University of New York College at Oneonta, Oneonta | 41 | 48 | 17 | 12649 | 21699 | 5311 | 75 | 17564 |
Iowa State University of Science and Technology, Ames | 81 | 37 | 17 | 9738 | 21610 | 6413 | 69 | 30062 |
University of South Florida, Tampa | 45 | 24 | 28 | 10598 | 19788 | 5966 | 52 | 21679 |
University of New Hampshire, Durham | 73 | 61 | 18 | 21947 | 35267 | 3955 | 76 | 35671 |
University of North Florida, Jacksonville | 51 | 20 | 21 | 9171 | 21922 | 5789 | 39 | 15300 |
University of South Carolina, Columbia | 70 | 46 | 19 | 14117 | 30301 | 5027 | 49 | 21811 |
State University of New York College at Brockport, Brockport | 42 | 42 | 18 | 12888 | 21938 | 5140 | 80 | 25733 |
The University of North Carolina at Chapel Hill, Chapel Hill | 32 | 76 | 14 | 6548 | 26374 | 11080 | 31 | 16165 |
Towson University, Towson | 57 | 40 | 17 | 11627 | 23139 | 7601 | 56 | 19069 |
University of California, Santa Barbara, Santa Barbara | 46 | 64 | 17 | 12711 | 34521 | 15389 | 47 | 17596 |
St. Mary's College of Maryland, St. Mary's City | 65 | 74 | 12 | 17696 | 29773 | 8664 | 70 | 17505 |
University of Georgia, Athens | 59 | 54 | 19 | 10288 | 28498 | 8970 | 45 | 15938 |
Christopher Newport University, Newport News | 60 | 42 | 17 | 15725 | 24947 | 5087 | 51 | 21572 |
The Ohio State University, Columbus | 68 | 49 | 19 | 12680 | 27575 | 7789 | 59 | 22830 |
University of Delaware, Newark | 54 | 62 | 12 | 15728 | 31998 | 6734 | 44 | 17200 |
California State Polytechnic University, Pomona, Pomona | 45 | 20 | 26 | 10701 | 21861 | 8280 | 35 | 16704 |
University of Illinois at Urbana–Champaign, Champaign | 67 | 67 | 16 | 14809 | 28951 | 10885 | 51 | 21543 |
Auburn University, Auburn University | 79 | 36 | 18 | 13057 | 27649 | 6733 | 46 | 24777 |
The University of Alabama, Tuscaloosa | 54 | 38 | 19 | 11584 | 24884 | 6680 | 53 | 26701 |
University of Wisconsin–Madison, Madison | 58 | 51 | 17 | 12733 | 28483 | 5857 | 48 | 22837 |
The University of Texas at Dallas, Richardson | 50 | 42 | 19 | 14068 | 31094 | 6664 | 41 | 17384 |
State University of New York at Binghamton, Binghamton | 40 | 66 | 21 | 13310 | 21420 | 6716 | 50 | 21110 |
Rutgers, The State University of New Jersey, New Brunswick/Piscataway, Piscataway | 59 | 53 | 15 | 15629 | 28291 | 9937 | 68 | 16766 |
University of Science and Arts of Oklahoma, Chickasha | 56 | 18 | 14 | 4132 | 11092 | 7098 | 29 | 15339 |
Miami University, Oxford | 79 | 68 | 17 | 19310 | 34482 | 6083 | 51 | 27315 |
University of Maryland, College Park, College Park | 44 | 63 | 18 | 12450 | 29821 | 6959 | 43 | 22696 |
New College of Florida, Sarasota | 53 | 57 | 10 | 5316 | 28345 | 10142 | 36 | 11458 |
The University of North Carolina at Asheville, Asheville | 77 | 30 | 14 | 7443 | 21075 | 6202 | 48 | 15443 |
University of Mary Washington, Fredericksburg | 77 | 68 | 15 | 12206 | 23934 | 6500 | 57 | 15600 |
University of California, Los Angeles, Los Angeles | 23 | 68 | 17 | 15397 | 38275 | 12777 | 45 | 16733 |
University of Virginia, Charlottesville | 33 | 85 | 16 | 5138 | 29460 | 16488 | 32 | 19384 |
University of California, Berkeley, Berkeley | 22 | 69 | 17 | 13164 | 36042 | 15863 | 41 | 16056 |
University of Oklahoma, Norman | 85 | 33 | 18 | 11417 | 22370 | 6011 | 52 | 21517 |
The University of North Carolina at Wilmington, Wilmington | 57 | 45 | 17 | 7367 | 19188 | 6792 | 25 | 19277 |
University of Connecticut, Storrs | 54 | 66 | 18 | 14403 | 31299 | 8167 | 63 | 23237 |
University of Michigan, Ann Arbor | 51 | 72 | 15 | 13170 | 38842 | 10783 | 46 | 27828 |
University of Colorado at Boulder, Boulder | 83 | 41 | 18 | 14549 | 35727 | 7873 | 43 | 19758 |
Calculation: Use following steps to find the models in Minitab:
Step 1: Enter the data into Minitab worksheet.
Step 2: Go to Stat, select Regression, again select Regression.
Step 3: Select AvgDebt as Response and all Predictors one by one.
The models for each explanatory variable, model standard deviation
Explanatory variable | Model | Model standard deviation s | P-value |
Admit, | |||
Yr4Grad | |||
StudPerFac | |||
InAfterAid | |||
OutAfterAid | |||
AvgAid | |||
PercBorrow |
Interpretation: The regression line for the variable AvgAid is having a negative slope which verifies the conclusion drawn from the scattered plot in part (a).
(c)
The variable which appears to be best single predictor of average debt.
(c)
Answer to Problem 14E
Solution: InAfterAid is best single predictor of average debt.
Explanation of Solution
The model of each explanatory variable, model standard deviation
The independent variable with smallest P-value is the significant predictor of the model. As the P-value is minimum for the explanatory variable InAfterAid which is
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