**Problem Recognition, Definition and Evaluation
**Just quite recently, my wife wanted me to buy a small television. She said that the television should be around 20 – 32 inch, and it should be a flat television.

So, now I need to get my wife a new television. Unfortunately, I am not sure how much the price of a television. So, I went to glodokshop.com to do a bit of research. The goal of research is to find out how much is the price of a small flat panel TV and how much is the reasonable price range for a television with certain characteristics. The data from glodokshop.com is tabulated in Table 1.

Brand | Size (inch) | resolution (px) | power consumption | audio output | weight (kg) | LED/ LCD | price (Rp, k) |

Polytron | 32 | 1366×768 | 135 | 10 | 12.5 | LCD | 2,800 |

Samsung | 32 | 1366×768 | 155 | 10 | 8.66 | LCD | 2,800 |

LG | 32 | 1366×768 | 120 | 10 | 9.2 | LCD | 2,900 |

LG | 32 | 1366×768 | 120 | 10 | 9.2 | LCD | 2,900 |

Samsung | 32 | 1366×768 | 30 | 10 | 8.7 | LCD | 3,100 |

Toshiba | 32 | 1366×768 | 26 | 20 | 5 | LCD | 2,950 |

Samsung | 32 | 1366×768 | 70 | 10 | 6 | LED | 3,100 |

Toshiba | 32 | 1366×768 | 55 | 20 | 5 | LED | 3,200 |

Samsung | 32 | 1366×768 | 70 | 20 | 10.9 | LCD | 3,400 |

LG | 32 | 1366×768 | 55 | 10 | 6.7 | LED | 3,251 |

Samsung | 32 | 1366×768 | 30 | 20 | 5.6 | LED | 3,324 |

Samsung | 32 | 1366×768 | 70 | 10 | 7.2 | LED | 3,800 |

Sanyo | 32 | 1366×768 | 100 | 20 | 9.8 | LCD | 4,000 |

Samsung | 32 | 1366×768 | 70 | 20 | 9 | LCD | 4,150 |

LG | 32 | 1366×768 | 129 | 20 | 9.2 | LCD | 4,200 |

Samsung | 32 | 1920×1080 | 40 | 20 | 5.6 | LED | 4,014 |

Toshiba | 32 | 1920×1080 | 39 | 20 | 9 | LED | 4,200 |

Samsung | 32 | 1920×1080 | 39 | 20 | 6.5 | LED | 4,600 |

Samsung | 32 | 1920×1080 | 80 | 20 | 10.2 | LED | 4,500 |

LG | 32 | 1920×1080 | 130 | 20 | 12 | LCD | 5,500 |

LG | 22 | 1366×768 | 55 | 200 | 4.2 | LCD | 1,575 |

LG | 22 | 1366×768 | 27 | 14 | 3.6 | LED | 1,650 |

LG | 22 | 1366×768 | 30 | 14 | 3.2 | LED | 1,760 |

Toshiba | 22 | 1920×1080 | 40 | 20 | 4.4 | LED | 1,850 |

Samsung | 22 | 1920×1080 | 22.4 | 6 | 3.5 | LED | 1,975 |

Polytron | 24 | 1920×1080 | 30 | 10 | 4.8 | LED | 1,950 |

Toshiba | 22 | 1920×1080 | 40 | 20 | 4.4 | LED | 2,000 |

Sanyo | 24 | 1366×768 | 57 | 6 | 5.5 | LCD | 1,750 |

Toshiba | 24 | 1366×768 | 65 | 20 | 8.5 | LCD | 1,900 |

Toshiba | 24 | 1920×1080 | 40 | 20 | 5.5 | LED | 2,300 |

LG | 32 | 1366×768 | 55 | 24 | 6.7 | LED | 3,220 |

Table 1. List of small size television price (Retrieved from www.glodokshop.com)

**Development of Feasible Alternatives
**Based on the information in Table 1, I need to find a formula which I can use to predict the TV price based on its screen size, panel type, panel resolution, weight, power consumption and audio output.

I replaced each non numeric parameter with a numeric value. The mapping is shown in Table 2.

Brand | resolution (px) | LED/LCD | |||

LG | 2 | 1366×768 | 2 | LCD | 2 |

Polytron | 3 | 1920×1080 | 3 | LED | 3 |

Samsung | 5 | ||||

Sanyo | 7 | ||||

Toshiba | 11 |

Table 2. Mapping of non-numeric parameter with numeric value

The result of the mapping is shown in Table 3.

Brand | Size (inch) | resolution (px) | power consumption | audio output | weight (kg) | LED/ LCD | price (Rp, k) |

5 | 32 | 2 | 135 | 10 | 12.5 | 2 | 2,800 |

6 | 32 | 2 | 155 | 10 | 8.66 | 2 | 2,800 |

3 | 32 | 2 | 120 | 10 | 9.2 | 2 | 2,900 |

3 | 32 | 2 | 120 | 10 | 9.2 | 2 | 2,900 |

6 | 32 | 2 | 30 | 10 | 8.7 | 2 | 3,100 |

10 | 32 | 2 | 26 | 20 | 5 | 2 | 2,950 |

6 | 32 | 2 | 70 | 10 | 6 | 3 | 3,100 |

10 | 32 | 2 | 55 | 20 | 5 | 3 | 3,200 |

6 | 32 | 2 | 70 | 20 | 10.9 | 2 | 3,400 |

3 | 32 | 2 | 55 | 10 | 6.7 | 3 | 3,251 |

6 | 32 | 2 | 30 | 20 | 5.6 | 3 | 3,324 |

6 | 32 | 2 | 70 | 10 | 7.2 | 3 | 3,800 |

7 | 32 | 2 | 100 | 20 | 9.8 | 2 | 4,000 |

6 | 32 | 2 | 70 | 20 | 9 | 2 | 4,150 |

3 | 32 | 2 | 129 | 20 | 9.2 | 2 | 4,200 |

6 | 32 | 3 | 40 | 20 | 5.6 | 3 | 4,014 |

10 | 32 | 3 | 39 | 20 | 9 | 3 | 4,200 |

6 | 32 | 3 | 39 | 20 | 6.5 | 3 | 4,600 |

6 | 32 | 3 | 80 | 20 | 10.2 | 3 | 4,500 |

3 | 32 | 3 | 130 | 20 | 12 | 2 | 5,500 |

3 | 22 | 2 | 55 | 200 | 4.2 | 2 | 1,575 |

3 | 22 | 2 | 27 | 14 | 3.6 | 3 | 1,650 |

3 | 22 | 2 | 30 | 14 | 3.2 | 3 | 1,760 |

10 | 22 | 3 | 40 | 20 | 4.4 | 3 | 1,850 |

6 | 22 | 3 | 22.4 | 6 | 3.5 | 3 | 1,975 |

5 | 24 | 3 | 30 | 10 | 4.8 | 3 | 1,950 |

10 | 22 | 3 | 40 | 20 | 4.4 | 3 | 2,000 |

7 | 24 | 2 | 57 | 6 | 5.5 | 2 | 1,750 |

10 | 24 | 2 | 65 | 20 | 8.5 | 2 | 1,900 |

10 | 24 | 3 | 40 | 20 | 5.5 | 3 | 2,300 |

3 | 32 | 2 | 55 | 24 | 6.7 | 3 | 3,220 |

Table 3. Mapping of Table 1 and Table 2

On the data in Table 3, a regression analysis was performed, for both linear and logarithmic analysis, to get the best fit formula. The linier regression would produce the following formula:

*Price = A x type + B x weight + C x audio + D x wattage + E x resolution + F x size + G x brand + H*

The logarithmic regression would produce the following formula:

*ln(Price) = (type x ln(A)) + (weight x ln(B)) + (audio x ln(C)) + (wattage x ln(D)) + (resolution x ln(E)) + (size x ln(F))+ (brand x ln(G))+ ln(H)*

**Development of outcomes for each alternative
**The linear regression analysis was carried out using MS Excel, and the result is shown at Table 4.

G | F | E | D | C | B | A | H |

47.660 | 85.838 | 2.521 | -2.111 | 869.044 | 190.139 | -25.417 | -4995.290 |

Table 4. Linear regression result on the data from Table 3

So, the linear regression formula is:

*Price = (-25.417 x brand) + (190.139 x size) + (869.044 x resolution) + (-2.111 x wattage) + (2.521 x audio) + (85.838 x weight) + (47.660 x panel type) – 4995.290*

The logarithmic regression analysis was carried out using MS Excel, and the result is shown at Table 5.

G | F | E | D | C | B | A | H |

1.035223 | 1.023973 | 1.00044392 | 0.99939 | 1.265946 | 1.0735 | 0.996411 | 172.7626 |

Table 5. Logarithmic regression result on the data from Table 3

So, the linear regression formula is:

*ln(Price) = (brand x ln(0.996411)) + (size x ln(1.0735)) + (resolution x ln(1.265946)) + (wattage x ln(0.99939)) + (audio x ln(1.00044392)) + (weight x ln(1.023973))+ (panel type x ln(1.035223))+ ln(172.7626)*

**Selection of Criterion
**The R2 value represents the coefficient of determination, which indicates how well the estimated Y (PRICE) compares to the actual Y (PRICE). The estimated Y is produced from the calculation, where the actual Y is from actual data. The value of R2 is between 0 and 1. In a perfectly fit situation, the estimated Y is equal to actual Y, making R2 equal to 1. The closer R2 to 1, the better the formula predicts the actual Y value.

**Analysis and Comparison of the Alternatives
**Based on the calculation, the R2 value for each option is as follow:

*Price = (-25.417 x brand) + (190.139 x size) + (869.044 x resolution) + (-2.111 x wattage) + (2.521 x audio) + (85.838 x weight) + (47.660 x panel type) – 4995.290;*R2= 0.827600612

*ln(Price) = (brand x ln(0.996411)) + (size x ln(1.0735)) + (resolution x ln(1.265946)) + (wattage x ln(0.99939)) + (audio x ln(1.00044392)) + (weight x ln(1.023973))+ (panel type x ln(1.035223))+ ln(172.7626);*R2= 0.895936057

**Selection of Preferred Alternatives
**As per the information above, the closer the R2 value to 1 is the second formula which is:

*ln(Price) = (brand x ln(0.996411)) + (size x ln(1.0735)) + (resolution x ln(1.265946)) + (wattage x ln(0.99939)) + (audio x ln(1.00044392)) + (weight x ln(1.023973))+ (panel type x ln(1.035223))+ ln(172.7626)*

Using the formula, the price for a certain type of television can be determined.

If I want to purchase a 32inch Toshiba with full HD resolution (1920×1080), wattage 50watt, with 20watt audio output, weight 10kg and LED panel, the price would be Rp5,691,000.

For a television with similar specification, but having Samsung brand, the price will be Rp 5,815,000.

Applying the formula and its standard deviation to the raw data, will provide information on which television is sold at cheap price, reasonable price and expensive price.

Table 6 shows the result.

Brand | Size (in) | res. (px) | power | audio | weight (kg) | LED/ LCD | price (Rp, k) | Est. Price (Rp,k) | Min Price (-1σ) | Max Price (+1σ) | Cheap? |

Polytron | 32 | 1366×768 | 135 | 10 | 12.5 | LCD | 2,800 | 3,538 | 3,111 | 4,024 | cheap |

Samsung | 32 | 1366×768 | 155 | 10 | 8.66 | LCD | 2,800 | 3,169 | 2,786 | 3,604 | in the range |

LG | 32 | 1366×768 | 120 | 10 | 9.2 | LCD | 2,900 | 3,314 | 2,913 | 3,769 | cheap |

LG | 32 | 1366×768 | 120 | 10 | 9.2 | LCD | 2,900 | 3,314 | 2,913 | 3,769 | cheap |

Samsung | 32 | 1366×768 | 30 | 10 | 8.7 | LCD | 3,100 | 3,421 | 3,008 | 3,891 | in the range |

Toshiba | 32 | 1366×768 | 26 | 20 | 5 | LCD | 2,950 | 3,088 | 2,715 | 3,512 | in the range |

Samsung | 32 | 1366×768 | 70 | 10 | 6 | LED | 3,100 | 3,243 | 2,851 | 3,688 | in the range |

Toshiba | 32 | 1366×768 | 55 | 20 | 5 | LED | 3,200 | 3,141 | 2,762 | 3,573 | in the range |

Samsung | 32 | 1366×768 | 70 | 20 | 10.9 | LCD | 3,400 | 3,533 | 3,107 | 4,019 | in the range |

LG | 32 | 1366×768 | 55 | 10 | 6.7 | LED | 3,251 | 3,363 | 2,957 | 3,825 | in the range |

Samsung | 32 | 1366×768 | 30 | 20 | 5.6 | LED | 3,324 | 3,305 | 2,906 | 3,759 | in the range |

Samsung | 32 | 1366×768 | 70 | 10 | 7.2 | LED | 3,800 | 3,336 | 2,933 | 3,794 | expensive |

Sanyo | 32 | 1366×768 | 100 | 20 | 9.8 | LCD | 4,000 | 3,356 | 2,951 | 3,817 | expensive |

Samsung | 32 | 1366×768 | 70 | 20 | 9 | LCD | 4,150 | 3,378 | 2,970 | 3,842 | expensive |

LG | 32 | 1366×768 | 129 | 20 | 9.2 | LCD | 4,200 | 3,310 | 2,911 | 3,765 | expensive |

Samsung | 32 | 1920×1080 | 40 | 20 | 5.6 | LED | 4,014 | 4,159 | 3,657 | 4,730 | in the range |

Toshiba | 32 | 1920×1080 | 39 | 20 | 9 | led | 4,200 | 4,414 | 3,881 | 5,021 | in the range |

Samsung | 32 | 1920×1080 | 39 | 20 | 6.5 | LED | 4,600 | 4,251 | 3,738 | 4,835 | in the range |

Samsung | 32 | 1920×1080 | 80 | 20 | 10.2 | LED | 4,500 | 4,527 | 3,980 | 5,149 | in the range |

LG | 32 | 1920×1080 | 130 | 20 | 12 | LCD | 5,500 | 4,475 | 3,935 | 5,090 | expensive |

LG | 22 | 1366×768 | 55 | 200 | 4.2 | LCD | 1,575 | 1,638 | 1,441 | 1,864 | in the range |

LG | 22 | 1366×768 | 27 | 14 | 3.6 | LED | 1,650 | 1,566 | 1,377 | 1,781 | in the range |

LG | 22 | 1366×768 | 30 | 14 | 3.2 | LED | 1,760 | 1,548 | 1,361 | 1,761 | in the range |

Toshiba | 22 | 1920×1080 | 40 | 20 | 4.4 | LED | 1,850 | 1,946 | 1,711 | 2,213 | in the range |

Samsung | 22 | 1920×1080 | 22.4 | 6 | 3.5 | LED | 1,975 | 1,955 | 1,719 | 2,224 | in the range |

Polytron | 24 | 1920×1080 | 30 | 10 | 4.8 | LED | 1,950 | 2,334 | 2,052 | 2,654 | cheap |

Toshiba | 22 | 1920×1080 | 40 | 20 | 4.4 | LED | 2,000 | 1,946 | 1,711 | 2,213 | in the range |

Sanyo | 24 | 1366×768 | 57 | 6 | 5.5 | LCD | 1,750 | 1,753 | 1,541 | 1,994 | in the range |

Toshiba | 24 | 1366×768 | 65 | 20 | 8.5 | LCD | 1,900 | 1,858 | 1,633 | 2,113 | in the range |

Toshiba | 24 | 1920×1080 | 40 | 20 | 5.5 | LED | 2,300 | 2,302 | 2,024 | 2,618 | in the range |

LG | 32 | 1366×768 | 55 | 24 | 6.7 | LED | 3,220 | 3,384 | 2,975 | 3,849 | in the range |

Table 6. Application of the formula to identify which televisions is in reasonable price, cheap and expensive.

Based on Table 6, a Polytron, 24 inch with Full HD, 30watt power consumption, 4.8kg of weight, and LED panel is consider cheap if it is sold with a price of Rp 1,950k.

**Performance monitoring and post evaluation result
**The formula should be good enough for the time being, as the data is limited. But, to make better formula, this formula should always be tested against actual cost from time to time. If the actual seems to be significantly different from the estimated value, the formula should be reviewed.

**References
**Dysert, L. R. (2012). Estimating. In S. Amos (Ed.), Skill & Knowledge of Cost Engineering (5th Ed.) (pp.9.1-9.34). USA: CreateSpace.

Television data and prices. (September 14, 2013). Retrieved from glodokshop.com

Toshiba television detail specifications. (September 14, 2013). Retrieved from toshiba.com

Samsung television detail specifications. (September 14, 2013). Retrieved from samsung.com

LG television detail specifications. (September 14, 2013). Retrieved from LG.com

Sanyo television detail specifications. (September 14, 2013). Retrieved from http://www.haier.com/ph/sanyoproduct/tv/

Sullivan, W. G., Wicks, E. M., & Koelling, C. P. (2012). Engineering Economy (15th Ed.) (pp. 67-94). New Jersey, United States: Prentice Hall.

AWESOME reposting, Pak Sadat!!!! Nice work!!! Now you are demonstrating that you know how to use these tools/techniques to help you make better decisions.

Keep up the good work and looking forward to seeing more postings like this in the future!!

BR,

Dr. PDG, Jakarta