, Data Analysis, and Decision Modeling - Statistics Project Example

Values Row Labels Sum of PRICE Count of SHOPS Sum of AGE Sum of SOLD Sum of TENNIS Sum of STORIES Sum of CRIME Sum of OCEAN 1-100 $29,079,575.00 72 1094 $144,757.00 13 84 216 6 101-200 $32,668,325.00 78 1144 $156,824.00 9 90 234 15 201-300 $29,471,301.00 72 1071 $144,750.00 9 88 216 14 301-400 $29,243,087.00 72 1116 $144,759.00 8 84 216 15 401-500 $34,026,462.00 80 1201 $160,833.00 9 92 240 8 501-600 $17,282,642.00 44 658 $88,464.00 7 50 132 3 Grand Total $171,771,392.00 418 6284 $840,387.00 55 488 1254 61 Task 1 A comprehensive summary of the data set Regression model Y= {A+Bx) +E} Y is predicted dependent variable Where A is a constant factor Bx is variable factor B is co-efficient corresponding to independent variable E is an error term SUMMARY OUTPUT Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 65535 Standard Error 0 Observations 2 ANOVA   df SS MS F Significance F Regression 7 0.5 0.071429 Residual 0 0 65535 Total 7 0.5         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -6.36259 0 65535 -6.36259 -6.36259 -6.36259 -6.36259 X Variable 5 0.000044 0 65535 0.000044 0.000044 0.000044 0.000044 The regression m model for the house price will therefore be Y=7+0.5R+0.071r Point prediction of the sales price anticipated to fetch Average market price and Age of the house Sum of PRICE     SIZE AGE Total 89-188 8 301028   9 427162   10 1503770   11 5606021   12 8165803   13 25149823   14 38821731   15 38270502   16 33324232   17 27868462   18 13582880   19 4392217   20 2497537   21 771190 89-188 Total   200682358 189-288 11 3017709   12 2096551   13 1922121   14 6877167   15 7163253   16 2894719   17 3192056   18 1065940   19 448386   20 469787 189-288 Total   29147689 389-488 8 3100000 389-488 Total   3100000 Grand Total   232930047 Our market intercept would therefore be 33271612 and the slope is 14. The explanation of the result is as follows: A 95% interval prediction for this sale price When the size of the house denoted as X is constant at the point X, and then we assume the mean to be the selling price which is denoted as Y which is linear around X, where bo which unknown factor intercept as well as b1 is the slope. b0 and b1 are thus two unknowns, but are approximated from the sample data average above. The approximates are indicated as b0 and b1. These data do not form a perfect line. This is not surprising, considering that our data are random (Ajit C. Tamhane 2000). In other words, if we assume equation (1) then our line predicts the mean for any given level x. However, when we actually take a measurement (i.e., observe the data), we observe The assumption in forecast the sales of the house is that the data doesn’t form a perfect line due to the fact that the data is random and thus the equation above forecast the mean for whichever given level of X. Nevertheless, it can be observed that the error is independent. The regression model for our sales forecast is Y=7+0.5R+0.071r The forecast interval is employed since we are 95% confident on the actual selling price of the house and thus our 95% prediction for the actual selling price is as follows (33,271,612+0.5(215) +t (0.07*10) +15(10) = $258.2 $258.2+33271.612} =33529.81 This is the best selling price for the house devoid of any other more information relating to the house price other than variables identified in the regression model above as provided. In making an estimated, we will employ the following formulae SSE/ (n-2)0.025} We employed 2 due to the degree of freedom that is the size of the house and the selling price. 33529.81/ (456-2) (0.025} =$1846.355± 33,529,810 An estimate of the marginal effect of house size on this sale price To examine the correctness of the model, it entails establishing if a specific variable such as housie size depict any effect on the selling price (Cowan 1998). Where there is an horizontal line (Slope zero) from the regression model, it implies that the selling price of the house is not affected by the size of the house since, there is no any link existing between an independent variable as well as the dependent variable we must anticipate to get b1 = 0. Assuming 95% confidence interval for b1 is given by 0.5± {15(456-2)*0.0025} =17.07± 0.5 We are therefore 95% confident that every extra square foot growth in price of the house between 18.23 and 17.07 Financial advice on whether John should use “W&M” or “A&B” to sell his house. Commission fee Selling price Commission Net selling price W$M 6% 33,529,810 2011.789 33,527,798 A$B 9% 33,529,810 3017.683 33,526,792 Mr. John should consider using W&M since, they charge a small commission to sell their house as observed ion the table above since, there a small impact on the net selling price of the house due to commission charged by the company. Task 3 Reflection of task 2 Task two majorly entailed the forecast of the house selling price that would be best for MR. John under the best and worst selling price in the market. We employed the time series data. That is the sales against the size of the house to predict the anticipated performance in terms of selling price. We then forecast the selling price of the house in the market by suing the data set provided specifically selecting their selling price, size, age as well as distance. We employed the data to predict the selling price by establishing the factors that recount to the variables to be forecasted such as the size and age of the house in the past and current economy. Unlikely, the list of houses in the dataset that correspond to this criterion might be quite small or it might not be a house of precise similarity as the one for Mr. John in comparison with those in the dataset (David Ruppert 2015). Other methodology is to take into consideration the selling price of the house in the region by using the average selling price in the data set. The factors that lead to dissimilar selling price as deposited in the data set is due to different house size. An initial model may hypothesize that the average in square foot worth per square foot of the house to be sold is $18.23-$17.07 with an average sell of $33,526,792. The estimated selling price of the house of size X might be {$33,526,792+$18.23X} which would therefore imply that a house of 215 Square foot might be forecasted to sell for $33,526,792+215(18.23) =$ 61,119,342.4. We are obviously certain that this just an estimation and thus the selling price of this house with 215 square foot is not probably going to sell at exactly $ 61,119,342.4.. The house price of this size might in reality range between $30,559,671.2 and $91,679,013.6. The determinant model is unsuitable; we must as a result take into consideration a probabilistic model (Evans 2013). Let Y be real selling price of the house. Then Y= [$33,526,792+0.5X+E} Were E is the error term which can either be positive or negative. The model will therefore be good where there is a small error term as well as the random term account for the entire variables that aren’t part of the model such as the distance in kilometers, the lot size, neighborhood and money variables that might affect the selling price. The worth of the error term differs from sale to sale of houses, as much as the house size is fixed. That is the house of similar size might sell for diverse prices (Ogden 2006). The interpretation of our regression equation in task two there implies that when X which is the size of the house is constant at a level x, then we the mean Y which is the selling price will be linear around the level x, where b0 is the unknown intercept and b1 is the unknown slope or change in Y per unit change in X and b0 and b1 are unknown precisely, but are predictable from test data. Their approximation is denoted b0 and b1. (Ogden 2006) Reference list Ajit C. Tamhane, ‎DD 2000, Statistics and Data Analysis: From Elementary to Intermediate, Springer, Sydney. Cowan, G 1998, Statistical Data Analysis, Cingage learning, London. David Ruppert, ‎SM 2015, Statistics and Data Analysis for Financial Engineering, John Wiley & Son's, New York. Evans, JR 2013, Statistics, Data Analysis, and Decision Modeling, John Wiley & Son's, New York. Ogden, T 2006, Essential Wavelets for Statistical Applications and Data., John Wiley & Son's, New York. RICE, JA 2006, Mathematical Statistics And Data Analysis, Cingage learning, London. Read More