solution to homework #1

Solution to Homework #1

MGS 8110, Regression & Forecasting Summer 2012

Solution HW #1 1MGS 8110

READING: Review the material in Lectures L00A, L00D, L00E & L00I. Read Chapters 2 of the textbook.Read Chapters 3 through 5. This is a lot of reading and you have 7

weeks to complete this reading assignment. Please step up and take a big bite out of it this week because you have minimal calculations to do this week (see below).

Submittals for this HW.The last worksheet in DATA HW01.xls is the Answer Sheet. Fill in the

blank cells and submit this sheet. Present 3 significant digits when appropriate. Hints are shown in Blue on the Answer Sheet. Eliminate the color coding before printing the Answer Sheet. Look over the Answer sheet before doing any calculation so that you know what is required.


Part A Access Class NotesDownload the class notes, homework, etc. from our Web page.

http://www.gsu.edu/~mgtrks/

Click on the MGS 8110, then Lecture 00. The downloads are PowerPoint presentations and can be printed 2 or 6 per page (in Power Point 2003 go to FILE/PRINT, then “Print what = handouts” and “Slides per page = 6”) (in Power Point 2007 go to View on toolbar, then / Handout Master / Slides Per Page /).


http://www.gsu.edu/~mgtrks/

Part B MS Equation Practice using MS Equation by duplicating the equations shown at the right. Change the x's to y's to verify that you used MS Equations and did not just cut-&-paste the box shown at the right. Submittal: Paste you three equations in one box on the right side of your Answer Sheet.

Stancell

HiPower

Acme

012.1

377.

975.

08.7

2

1,:

2

4

2

2

1

2

Life

eXN

a

acbbX

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Part C Basic Excel Calculations

C0. Access the Osyter Data in the first worksheet of DATA HW01.xls. The definition of the variables is given in the second worksheet.

C1. Create an exact copy of the date in the first worksheet. That is, make a duplicate copy of the 1st worksheet. Label the tab for the first worksheet "DATA - original". Label the tab for the third worksheet "DATA - Analysis #1".

C2. Create an "Index Column" at the far left of the data array. Each row of data should be given a sequential number from 1 to 30.

C3. Make a duplicate copy of the data in the third worksheet and label the tab of the fourth worksheet "DATA - Analysis #2".

Until told different, you should be doing the subsequent calculations in the worksheet, DATA - Analysis #1. This is the first of the two new worksheets.

C4. Create four cells at the bottom of the column of data and calculate the Mean, Standard Deviation, Skewness and Kurtosis for Weight, Volume, 3D & 2D. Which of variables appears to be Normally Distributed.

C5. Create a column to the right of the 2D column and classify the oysters by volume. Label the column "Class". Less than 10 cc is "S" (Small), 10 to 13 cc is "M" (Medium) and greater than 13 is "L" (Large). Use a nested IF command.

C6. Add three cells at the bottom of the Class column and state the number of Small, Medium and Large oysters in the sample. Use the COUNTIF command in Excel.

C7. Add two columns to the right of the “Class” and convert the Weight in grams to Weight in ounces and convert the volume in cc to volume in fluid ounces. Label the columnsWt_oz and Vol_oz.

C8. Add another column to the right of Vol_oz column and calculate the Ratio of Weight to Volume. State these values as percentages. Title the column "Ratio WtVol". Does it matter if you use the two columns with metric units or the two columns with US units?

C9. Create three cells at the bottom of the Ratio WtVol column and calculate the 1st Quartile, 2nd Quartile and 3rd Quartile. Use the Excel command QUARTILE.

C10. Create a fourth cell at the bottom of the Ratio WtVol column and calculate the 90th Percentile. Use the Excel command PERCENTILE.

C11 Add another column to the right of the Ratio WtVol column. Print the rank of each oyster in terms of volume. The oyster with a rank of 1 has the highest volume of the 30 oysters. Use the RANK function. Title the column "Rank.Vol".

C12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1) Median, 2) Percentage for the Mean, 3) Percentage for the Median and 4) the Difference between the Percentage Mean and Percentage Median. HINT: use the PercentRank function in Excel to calculate the two percentage rows, that is for 2) and 3).

C13. Based on the difference between the % Mean and the % Median, is Pixels_3D normally distributed? Base on the calculated values of Skewness and Kurtosis is Pixels_3D normally distributed?






Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D1 12.92 13.04 5136699 479072 11.4 11.71 4795151 414583 17.42 17.42 6453115 608914 6.79 7.23 2895239 299495 9.62 10.03 3672746 416166 15.5 15.59 5728880 480707 9.66 9.94 3987582 347178 7.02 7.53 2678423 272309 12.56 12.73 5481545 5271210 12.49 12.66 5016762 4150011 10.12 10.53 3942783 3121612 10.64 10.84 4052638 4185213 12.99 13.12 5334558 4460814 8.09 8.48 3527926 3534315 14.09 14.24 5679636 4748116 10.73 11.11 4013992 4097617 15.17 15.35 5565995 6536118 15.5 15.44 6303198 5091019 5.22 5.67 1928109 2289520 7.75 8.26 3450164 3480421 10.71 10.95 4707532 3715622 7.91 7.97 3019077 2907023 6.93 7.34 2768160 2459024 13.63 13.21 4945743 4808225 7.67 7.83 3138463 3211826 11.27 11.38 4410797 4511227 10.98 11.22 4558251 3702028 8.87 9.25 3449867 3933329 13.68 13.75 5609681 5135130 14.27 14.37 5292105 53281




Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D1 12.92 13.04 5136699 479072 11.4 11.71 4795151 414583 17.42 17.42 6453115 608914 6.79 7.23 2895239 299495 9.62 10.03 3672746 416166 15.5 15.59 5728880 480707 9.66 9.94 3987582 347178 7.02 7.53 2678423 272309 12.56 12.73 5481545 5271210 12.49 12.66 5016762 4150011 10.12 10.53 3942783 3121612 10.64 10.84 4052638 4185213 12.99 13.12 5334558 4460814 8.09 8.48 3527926 3534315 14.09 14.24 5679636 4748116 10.73 11.11 4013992 4097617 15.17 15.35 5565995 6536118 15.5 15.44 6303198 5091019 5.22 5.67 1928109 2289520 7.75 8.26 3450164 3480421 10.71 10.95 4707532 3715622 7.91 7.97 3019077 2907023 6.93 7.34 2768160 2459024 13.63 13.21 4945743 4808225 7.67 7.83 3138463 3211826 11.27 11.38 4410797 4511227 10.98 11.22 4558251 3702028 8.87 9.25 3449867 3933329 13.68 13.75 5609681 5135130 14.27 14.37 5292105 53281

Mean = 11.05 11.27 4,384,827 44364.20St Dev = 3.10 2.96 1,169,077 10289.51Skewness = 0.07 0.08 -0.16 0.28Kurtosis = -0.79 -0.74 -0.82 -0.15Normal ? Yes Yes Yes Yes

=AVERAGE(B2:B31)

=STDEV(C2:C31)

=SKEW(D2:D31)

=KURT(E2:E31)

=IF(AND(B35>=-1,B35<=1,B36>=-1,B36<=1),"Yes","NO")






Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D Class Wt_oz Vol_oz1 12.92 13.04 5136699 47907 L 0.456 0.4412 11.4 11.71 4795151 41458 M 0.402 0.3963 17.42 17.42 6453115 60891 L 0.614 0.5894 6.79 7.23 2895239 29949 S 0.240 0.2445 9.62 10.03 3672746 41616 M 0.339 0.3396 15.5 15.59 5728880 48070 L 0.547 0.5277 9.66 9.94 3987582 34717 S 0.341 0.3368 7.02 7.53 2678423 27230 S 0.248 0.2559 12.56 12.73 5481545 52712 M 0.443 0.43010 12.49 12.66 5016762 41500 M 0.441 0.42811 10.12 10.53 3942783 31216 M 0.357 0.35612 10.64 10.84 4052638 41852 M 0.375 0.36713 12.99 13.12 5334558 44608 L 0.458 0.44414 8.09 8.48 3527926 35343 S 0.285 0.28715 14.09 14.24 5679636 47481 L 0.497 0.48216 10.73 11.11 4013992 40976 M 0.378 0.37617 15.17 15.35 5565995 65361 L 0.535 0.519

=IF(C2<=10,"S",IF(C2>13,"L","M"))

OR

=IF(C2<=10,"S",IF(C2<13,"M",IF(C2>13,"L","***")))

=B2*gmToz

OR

=B2*$G$40

=C2*ccToz

OR

=C2*$G$41


gm to oz 0.035274 "gmToz"

cc to oz 0.033814 "ccToz"

S 0.244 0.248L 0.481 0.447S 0.271 0.265M 0.398 0.385M 0.387 0.379S 0.313 0.313L 0.483 0.465L 0.503 0.486

101010

=COUNTIF($F$2:$F$31,"S")

=COUNTIF($F$2:$F$31,"L")







Rank Vol0.991 1.033576 100.974 1.015559 131.000 1.043176 10.939 0.97969 290.959 1.000533 200.994 1.037153 20.972 1.01379 210.932 0.972522 270.987 1.029245 110.987 1.029168 120.961 1.002558 190.982 1.023929 180.990 1.032839 90.954 0.995199 230.989 1.032187 60.966 1.007495 160.988 1.030943 41.004 1.047229 30.921 0.960384 300.938 0.978766 240.978 1.020311 170.992 1.035322 250.944 0.984906 281.032 1.076342 80.980 1.021859 260.990 1.033092 140.979 1.020862 150.959 1.000321 220.995 1.037865 70.993 1.035916 5

0.960 1.001 10.981 1.023 20.991 1.033 30.9954 1.0384 Percentile 90%

Ratio WtVol

=Weight/Volume)

=G2/H2

=QUARTILE(I$2:I$31,$K33)

why the $ signs

=PERCENTILE(J2:J31,0.9)

=RANK(C2,Volume)

or

=RANK(Volume,Volume)





C3. Make a duplicate copy of the data in the third worksheet and label the tab of the fourth worksheet "DATA - Analysis #2".

Until told different, you should be doing the subsequent calculations in the worksheet, DATA - Analysis #1. This is the first of the two new worksheets.









C12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1) Median, 2) Percentage for the Mean, 3) Percentage for the Median and 4) the Difference between the Percentage Mean and Percentage Median. HINT: use the PercentRank function in Excel to calculate the two percentage rows, that is for 2) and 3).



Part C Basic Excel CalculationsC12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1)

Median, 2) Percentage for the Mean, 3) Percentage for the Median and 4) the Difference between the Percentage Mean and Percentage Median. HINT: use the PercentRank function in Excel to calculate the two percentage rows, that is for 2) and 3).



Mean = 11.05 11.27 4,384,827 44364.20St Dev = 3.10 2.96 1,169,077 10289.51Skewness = 0.07 0.08 -0.16 0.28Kurtosis = -0.79 -0.74 -0.82 -0.15Normal ? Yes Yes Yes Yes

Median = 4,484,524% Mean 48.0%

% Median 50.0%Difference -2.0%

=MEDIAN(Vol3D)

=PERCENTRANK(Vol3D,D33)

=PERCENTRANK(Vol3D,D39) =D40-D41

Part D Population Differences Now go to the worksheet, DATA - Analysis #2.

D1. Sort the data in terms of the Class.. You are creating three sub populations: Small, Medium and Large. In Excel click on the Data icon on the uppermost toolbar, then click on Sort.

D2. Calculate the Average, Standard Deviation and the Coefficient of Variation for "Volume in cc" for each of the three sub-populations.

D3. How good are these estimate of the Means? Calculate a 95 % confidence interval for each of the three means..


Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D Class Mean StDev Coef Var4 6.79 7.23 2895239 29949 S 7.950 1.169 0.1477 9.66 9.94 3987582 34717 S8 7.02 7.53 2678423 27230 S 7.210 L CI for Mean14 8.09 8.48 3527926 35343 S 8.690 U CI for Mean19 5.22 5.67 1928109 22895 S20 7.75 8.26 3450164 34804 S22 7.91 7.97 3019077 29070 S23 6.93 7.34 2768160 24590 S25 7.67 7.83 3138463 32118 S28 8.87 9.25 3449867 39333 S2 11.4 11.71 4795151 41458 M 11.316 0.860 0.0765 9.62 10.03 3672746 41616 M9 12.56 12.73 5481545 52712 M 10.772 L CI for Mean10 12.49 12.66 5016762 41500 M 11.860 U CI for Mean11 10.12 10.53 3942783 31216 M12 10.64 10.84 4052638 41852 M16 10.73 11.11 4013992 40976 M21 10.71 10.95 4707532 37156 M26 11.27 11.38 4410797 45112 M27 10.98 11.22 4558251 37020 M1 12.92 13.04 5136699 47907 L 14.553 1.400 0.0963 17.42 17.42 6453115 60891 L6 15.5 15.59 5728880 48070 L 13.668 L CI for Mean13 12.99 13.12 5334558 44608 L 15.438 U CI for Mean15 14.09 14.24 5679636 47481 L17 15.17 15.35 5565995 65361 L18 15.5 15.44 6303198 50910 L24 13.63 13.21 4945743 48082 L29 13.68 13.75 5609681 51351 L30 14.27 14.37 5292105 53281 L

=AVERAGE($C2:$C11)

=STDEV($C12:$C21)

=H22/G22

=G2-2*H2/SQRT(10)

=G2+2*H2/SQRT(10)

=G22-2*H22/SQRT(10) = 13.668

or

=$G$22-NORMSINV(0.975)*$H$22/SQRT(10) = 13.685

or

=$G$22-TINV(0.05,9)*$H$22/SQRT(10) = 13.552

Part E Data Analysis Add-inE0. Load the Add-in "Data analysis" to your Excel (see slides 44 thru 50 of L00D).

Access the Oyster Data. E1. Use / Data Analysis / Descriptive Statistics to calculate basic statistics for th four

variables: Weight, Volume, 3D and 2D.


Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D

Mean 11.1 11.3 4,384,827 41,287Standard Error 0.566 0.541 213,443 1,879Median 10.9 11.2 4,484,524 41,479Mode 15.5 #N/A #N/A #N/AStandard Deviation 3.10 2.96 1,169,077 10,290Sample Variance 9.60 8.78 1,366,740,731,439 105,874,081Kurtosis -0.792 -0.741 -0.825 -0.155Skewness 0.074 0.077 -0.157 0.278Range 12.2 11.8 4,525,006 42,466Minimum 5.2 5.7 1,928,109 22,895Maximum 17.4 17.4 6,453,115 65,361Sum 331.6 338.2 131,544,817 1,238,609Count 30 30 30 30

Part E Data Analysis Add-inE2. Calculate the correlation between 4 variables using / Data Analysis / Correlation / in

Excel.


Weight_g Volume_cc Pixels_3D Pixels_2DOyster_Weight_g 1.000Oyster_Volume_cc 0.999 1.000Pixels_3D 0.976 0.977 1.000 Pixels_2D 0.918 0.920 0.893 1.000

Part F Normal DistributionThe transaction time at an ATM is approximately normally distributed with a mean of 20

seconds and a standard deviation of 8 seconds.F1. What is the probability that a transaction takes more than 30 seconds?F2. What is the probability that a transaction takes more than 35 seconds?F3. What is the probability that a transaction takes less than 15 seconds?F4. What is the probability that a transaction takes between 15 and 25 seconds?F5. Ten percent of the customers will have a transaction time greater than what value

(in seconds)?


Part F Normal Distribution The transaction time at an ATM is approximately normally distributed with a mean of 20 seconds and a standard deviation of 8 seconds.

F1. What is the probability that a transaction takes more than 30 seconds?F2. What is the probability that a transaction takes more than 35 seconds?F3. What is the probability that a transaction takes less than 15 seconds?F4. What is the probability that a transaction takes between 15 and 25 seconds?F5. Ten percent of the customers will have a transaction time greater than what value

(in seconds)?F6. Calculate a so-called 95% Confidence interval for transaction times, that is calculate

the 2.5 percentile point and the 97.5 percentile point.F7. In class you were told that you could frequently approximate a 95% Confidence

Interval by multiplying the standard deviation by 2 and then adding and subtracting that from the average. The actual formula is shown below. Calculate this approximate 95% CI.


XXCI 295. 0.106 =1-NORMDIST(30,20,8,1)0.030 =1-NORMDIST(35,20,8,1)0.266 =NORMDIST(15,20,8,1)0.468 =NORMDIST(25,20,8,1)-NORMDIST(15,20,8,1)

30.3 =NORMINV(0.9,20,8)4.32 =NORMINV(0.025,20,8)35.68 =NORMINV(0.975,20,8)

4.00 =20-2*836.00 =20+2*8

Answer Sheet


B Paste your MS Equations somewhere on this Answer Sheet.

0.106 =1-NORMDIST(30,20,8,1)0.030 =1-NORMDIST(35,20,8,1) Average

0.266 =NORMDIST(15,20,8,1) St Dev

0.468 =NORMDIST(25,20,8,1)-NORMDIST(15,20,8,1) Skewness

Kurtosis

30.3 =NORMINV(0.9,20,8) Normally distributed?

4.32 =NORMINV(0.025,20,8)35.68 =NORMINV(0.975,20,8) Rank Vol

0.991 1.033576 104.00 =20-2*8 0.974 1.015559 1336.00 =20+2*8 1.000 1.043176 1

4 S 0.240 0.244 0.939 0.97969 295 M 0.339 0.339 0.959 1.000533 206 L 0.547 0.527 0.994 1.037153 27 S 0.341 0.336 0.972 1.01379 218 S 0.248 0.255 0.932 0.972522 279 M 0.443 0.430 0.987 1.029245 1110 M 0.441 0.428 0.987 1.029168 1211 M 0.357 0.356 0.961 1.002558 1912 M 0.375 0.367 0.982 1.023929 1813 L 0.458 0.444 0.990 1.032839 914 S 0.285 0.287 0.954 0.995199 2315 L 0.497 0.482 0.989 1.032187 616 M 0.378 0.376 0.966 1.007495 1617 L 0.535 0.519 0.988 1.030943 418 L 0.547 0.522 1.004 1.047229 319 S 0.184 0.192 0.921 0.960384 3020 S 0.273 0.279 0.938 0.978766 2421 M 0.378 0.370 0.978 1.020311 1722 S 0.279 0.269 0.992 1.035322 2523 S 0.244 0.248 0.944 0.984906 2824 L 0.481 0.447 1.032 1.076342 825 S 0.271 0.265 0.980 1.021859 2626 M 0.398 0.385 0.990 1.033092 1427 M 0.387 0.379 0.979 1.020862 1528 S 0.313 0.313 0.959 1.000321 2229 L 0.483 0.465 0.995 1.037865 730 L 0.503 0.486 0.993 1.035916 5

C5 Excel IF statement used for the first cell in the Class column.

C6 Excel COUNTIF statement used for the Small count.

C9 & C10 0.960 1.001 1st Quartile C12 4,484,524 Median0.981 1.023 2nd Quartile 48.0% % Mean0.991 1.033 3rd Quartile 50.0% % Median0.9954 1.0384 90th Percentile -2.0% Difference

C13 Yes of No Normally Distributed based on difference between Mean and Median?Yes of No Normally Distributed based on Skewness & Kurtosis?

D2 & D3 Small Medium Large

7.950 11.316 14.553 Mean

7.210 10.772 13.668 Lower limit

8.690 11.860 15.438 Upper Limit

0.147 0.076 0.096 Coeficient of Variation

E Weight_g Volume_cc Pixels_3D Pixels_2D F1 0.106 Prob (t > 30)

Mean 11.1 11.3 4,384,827 41,287 F2 0.030 Prob (t > 35)

Standard Error 0.566 0.541 213,443 1,879 F3 0.266 Prob (t < 15)

Median 10.9 11.2 4,484,524 41,479 F4 0.468 Prob (15 < t < 25)

Mode 15.5 #N/A #N/A #N/A F5 30.3 t upper 10%

Standard Deviation3.10 2.96 1,169,077 10,290 F6 4.3 lower CI

Sample Variance 9.60 8.78 1,366,740,731,439 105,874,081 35.7 upper CI

Kurtosis -0.792 -0.741 -0.825 -0.155 F7 4.0 lower CI

Skewness 0.074 0.077 -0.157 0.278 36.0 upper CI

Range 12.2 11.8 4,525,006 42,466Minimum 5.2 5.7 1,928,109 22,895Maximum 17.4 17.4 6,453,115 65,361Sum 331.6 338.2 131,544,817 1,238,609Count 30 30 30 30

Hints are shown in blue.

Ratio WtVol

solution to homework #1

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