STAT6003. Statistics for Financial Decisions

This assesment can be based on several theories and methods. Please use Excel for statistical analysis in this assessment. Relevant Excel statistical output must be properly analThe word limit for this group assignment is

The variables for this assignment are as follows: V1) Market Price ($000) V2) Sydney price Index V3) Total number of square meters V4) Age of house (years)

Task 1: Selecting your Random Sample and Creating your Sample Data File . In order to select the sample data that will form the basis of your assignment you will need to make use of the random number table provided with this assignment. The provided table of random numbers is, as the title suggests, a sequence of randomly generated numerical digits (0 to 9). These digits are arranged in a table with one hundred rows numbered 01 to 00 and twenty columns spread over two pages. The entries in each column of each row consist of five single digits. The property data from which you will select your sample data consists of 400 IDs each with an identifying property number (PN) ranging from 1 (or 001) to 400. Your first task is to select 50 three digit random (property) numbers ranging from 001 to 400 from the provided table of random numbers. We will ask you to select 50 numbers, to begin with, just to cover the distinct possibility that you may select the same three digit number more than once. The type of simple random sampling that we will be engaged in here is termed "without replacement" because we specifically do not want to allow a property identification number to be selected more than once. In order to select your 50 random property identification numbers you will need to first go to a starting position row and column in the random number table. Defined by the last three digits of your Torrens University student identification number. The last two digits of your Torrens ID number identifies the row and the third last digit identifies the column of your (relatively) "unique" starting position. STAT6003 Assessment 4 Brief Case Study Individual For the demonstration last three digits of 312, reading across row 12 from left to right starting at column 3 as instructed, you would encounter the following three digit numbers; 293 313 381 349 656 985 295 You need to record these first three acceptable ID numbers, 293, 313, 381 and 349 into the first column of an Excel spread-sheet and then continue this process until fifty valid three-digit personal identification numbers selected.

Task 2:

1. Provide the complete summary statistics for Market Price ($000) and Age of house (years).

2. Describe the shape of the distributions for Market Price ($000) and Age of house (years).

3.Test whether the population's average Market Price ($000) is different from 777.

4.Construct a 95% confidence interval for the Market Price ($000), also Interpret the confidence interval.

5.Provide an introduction section on the rationale of your model , sample size, and the dependent and independent variables (including their unit of measurement) in this model.

6.Plot the dependent variable against each independent variable using scatter plot/dot function in Excel. Examine these scatter plots and correctly assess the strength and the nature of the relationship between the dependent and the independent variables?

7.Present the multiple regression model with complete regression summary output in your assignment.

8.Provide the simple linear regression data analysis for the market price as the response variable and the Land size in Square meters as the explanatory variable. Write down the least square regression equation and correctly interpret the equation.

9. clear interpretation of the slope of the regression line from question 8. You must refer to the variables of interest.

10.What is the value of the coefficient of determination for the relationship between the dependent and independent variable from question 8. Interpret this value accurately and inSTAT6003 Assessment 4 Brief Case Study Individual a meaningful way.

11.State the 95% confidence interval for the slope coefficient and interpret this interval from question 8. (5 Marks) 12.Compare the multiple regression model (question 7) and simple linear regression model (question 8) and evaluate the goodness of fit between these two modelling techniques.

13.Predict the market price of a house (in $) with a building area of 300 square meters. Explain why your answer is valid.

14.By performing an appropriate hypothesis test what decision and conclusion would you draw about the hypothesis that the Land size in Square meters useful in predicting the market price of a house (in $)? Use the data provided to justify your answer, as appropriate. When answering this research question.

15.For statistical analysis involving hypothesis testing in this assignment, you are required to: Formulate the null and alternative hypotheses for full model. State your statistical decision using significant value () of 5% for this test. State your conclusion in this context.

Table of Random Numbers 3 5 8 9 Row 2 11164 36318 75061 37674 26320 75100 10431 20418 19228 91792 21215 91791 76831 58678 87054 31687 93205 43685 19732 08468 66558 08882 90870 41810 01806 02977 44482 37649 12462 UAWN- 10438 50564 36792 26236 33266 66583 60881 97395 20461 36742 02852 67497 73944 04773 12032 51414 82384 38370 00249 80709 72605 78483 72717 68714 18048 25005 04151 49563 12872 14063 93104 64208 48237 41701 73 117 33242 42314 83049 21933 92813 04763 29341 80749 80151 33835 52602 79147 08868 10 00 - 51486 72875 38605 04638 09227 10606 99756 26360 64516 17971 48478 09610 17141 55217 13015 72907 00431 45117 33827 92873 02953 85474 71325 53010 94601 15838 16805 61004 43516 17020 11 65285 97198 12138 65692 98566 29550 12 17264 57327 38224 29301 31381 38109 34976 68368 04985 51092 37780 40261 13 95639 99754 92558 14479 31 199 14 61555 76404 86210 11808 12841 45147 97438 60022 12645 62000 04689 87130 79225 08153 84967 64539 79493 74917 15 78137 98768 14733 24550 28067 68894 38490 16 62490 99215 84987 28759 19177 07044 92729 37284 13211 37485 10415 3645 17 24216 63444 21283 46999 98501 18 16975 95428 33226 55903 31605 43817 22250 03918 71 168 57609 91510 77904 74244 50940 62562 19 59138 39542 31553 49862 96566 48825 20 29478 59652 50414 31966 87912 87154 12944 21 96155 95009 27429 72918 08457 78134 48407 26061 58754 05326 12468 20245 14015 04014 35713 03980 03024 22 29621 66583 62966 64629 63293 53307 48766 23 12639 75291 71020 7265 41598 64074 24 14544 37134 54714 2401 63228 26831 19386 15457 17999 18306 04711 34593 22561 25 83403 88827 09834 11333 68431 31706 26652 35434 09532 26 67642 05204 30697 44806 96989 68403 85621 45556 27 64041 99011 14610 40273 09482 62864 01573 82274 81446 32477 97444 16936 39384 97551 09620 63932 03091 17048 94523 59904 20963 29 89416 52795 10631 09728 68202 02477 55494 39563 93039 50985 97593 34320 30 82244 34392 96607 17220 51984 10753 76272 96990 55244 70693 25255 40029 23289 48819 07159 60172 81697 31 20712 32 09119 74803 97303 88701 51380 73143 98251 78635 27556 57666 41204 47589 78364 38266 94393 70713 53388 79865 92069 33 12923 53712 8777 34 46492 61594 26729 58272 81754 14648 77210 39355 74816 03363 35 08433 19172 08320 20839 13715 10597 17234 57929 36 10011 75004 86054 41 190 10061 19660 03500 68412 57812 84750 10115 69220 37 92420 65431 16530 05547 10683 88102 30176 07304 43233 82976 47981 46588 38 35542 55865 47010 57022 52161 69395 41387 87195 39 86595 26247 18552 29491 33712 32285 64844 34985 58036 99137 47482 06204 24138 24272 16196 04393 40 72115 51343 70958 96768 74317 27176 29600 41 07428 58863 96023 88936 28906 55013 26937 48174 04197 36074 65315 12537 42 35379 27922 26299 23593 64629 57801 10437 43965 15344 43 10982 22807 10920 77806 15444 49244 47277 11346 15884 28131 44 90127 33341 12446 45 63002 12990 23510 68774 48983 20481 59815 67248 17076 78910 45389 54847 77919 41 105 46 40779 86382 48454 65269 91239 45989 84631 94058 82458 15139 76856 86019 47928 47 43216 12608 18167 93643 09204 98855 59051 56492 11933 64958 48 96167 64375 74108 32989 24843 01 128 74658 49 70975 62693 35684 72607 23026 37004 61875 23570 75754 29090 40264 80399 47254 40135 69916 50 85812Table of Random Numbers 6 8 Row 0 2 3 40603 16152 83235 37361 98783 24838 39793 80954 76865 32713 51 60916 71018 90561 84505 53980 64735 85140 52 10941 53585 69958 13526 53 73505 83472 55953 17957 11446 22618 34771 25777 27064 54 39412 16013 11442 89320 11307 49396 39805 12249 57656 88686 55 57994 76748 54627 48511 78646 33287 35524 54522 08795 56273 25942 56 61834 59199 15469 82285 84164 91333 90954 87186 31598 18443 76162 51146 57 91402 77227 79516 21007 58602 81418 87838 83880 20125 10794 37780 61705 18276 99041 78135 99661 58 58299 63839 71371 32392 51812 48248 96419 59 40684 99948 33880 76413 74452 49954 60 75978 64298 08074 62055 73864 01926 78374 15741 39861 88267 76068 62445 64361 78685 24246 27027 48239 34556 25067 77571 98608 4984 $5990 57048 77974 37634 81564 37224 90374 86203 29677 82543 37554 89179 16381 15069 25416 87875 78352 67913 09245 47773 51272 06976 99571 33365 64 52458 88880 65 33007 85607 92008 44897 24964 50559 79549 85658 96865 24186 05866 66269 43158 66 38712 31512 08588 61490 72294 42862 87334 58722 03678 69602 34625 75958 56869 17907 81867 11535 67 2618 69497 51351 47799 20477 71786 52560 66827 79419 70886 58 12893 54048 07255 86149 99090 70958 50775 31768 52903 27645 69 40229 19209 74939 70 33186 81346 85095 $7282 85536 72661 32180 71 79893 29448 88392 54211 61708 83452 61227 81690 42265 20310 30120 82443 11152 72 48449 15102 44126 19438 23382 14985 37538 04259 68983 50561 06902 10269 22216 70210 60736 58772 73 94205 09278 81313 77400 41 126 52614 93613 27263 99381 49500 74 38648 81009 05114 75 04292 46028 75666 26954 34979 68381 45154 09314 40899 76 17026 49737 85875 12139 59391 81830 30185 83095 78752 74842 85522 74092 77 48070 76848 02531 97737 10151 18169 31709 78 30159 95450 83778 46115 99178 97718 98440 15076 21 199 20492 12148 92231 31361 60650 54695 30035 22765 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