W2_SSD_Estimated Cost of a Television

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 research is to find out how much is the price of a small flat panel TV. I decided that the TV should be a Toshiba with either LCD or LED panel, between 20 inch until 32 inch, and with either 1366×768 panel resolution or 1920×1080 panel resolution. The list is shown in Table 1.

 SIZE RESOLUTION LED/LCD PRICE (Rp, k) 22 1920×1080 LED 1,850 22 1920×1080 LED 2,000 24 1366×768 LCD 1,900 24 1920×1080 LED 2,300 29 1366×768 LED 3,500 32 1366×768 LCD 2,950 32 1366×768 LED 3,200 32 1920×1080 LED 4,200

Table 1. List of small size Toshiba 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 and panel resolution. By replacing the LED value to 3, the LCD value to 2, the 1920×1080 value to 2073600 and 1366×768 to 1049088, I created these following Table 2 and Table 3.

 SIZE RESOLUTION LED/LCD PRICE (Rp, k) 22 2073600 2 1,850 22 2073600 3 2,000 24 1049088 2 1,900 24 2073600 3 2,300 29 1049088 3 3,500 32 1049088 2 2,950 32 1049088 3 3,200 32 2073600 3 4,200

Table 2. Standard modified television data vs price

 SIZE2 RESOLUTION2 TYPE2 PRICE (Rp, k) 484 4.29982E+12 4 1,850 484 4.29982E+12 9 2,000 576 1.10059E+12 4 2,000 576 4.29982E+12 9 2,300 841 1.10059E+12 9 3,500 1024 1.10059E+12 4 2,950 1024 1.10059E+12 9 3,200 1024 4.29982E+12 9 4,200

Table 3. Squared television data vs price

With Table 2, I tried to find the best fit formula using regression analysis, for both linier and logarithmic. The linier regression will produce the following formula:

Price = A x size + B x resolution + C x type + D

The logarithmic regression will produce the following formula:

ln(Price) = (size x ln(A)) + (resolution x ln(B)) + (type x ln(C))+ ln(D)

Table 3 shows the square of each of the factor. The linier regression for Table 3 will produce the following formula:

Price = A x size2 + B x resolution2 + C x type2 + D

The logarithmic regression for Table 3 will produce the following formula:

ln(Price) = (size2 x ln(A)) + (resolution2 x ln(B)) + (type2 x ln(C))+ ln(D)

Development of outcomes for each alternative

Using MS Excel Linest() function on Table 2, the result is shown at Table 4.

 C B A D 398.949 0.000337169 175.334352 -3592.12272

Table 4. Linier regression result for non-squared data

Price = 175.334352 x size + 0.000337169 x resolution + 398.949 x type -3592.12272

Using MS Excel Logest() function on Table 2, the result is shown at Table 5.

 C B A D 1.17545 1.000000081 1.06418144 279.7372771

Table 5. Logaritmic regression result for non-squared data

ln(Price) = (size x ln(1.06418144)) + (resolution x ln(1.000000081)) + (type x ln(1.17545))+ ln(279.7372771)

 C B A D 82.6009 8.08258E-11 3.06279442 -366.507499

Table 6. Linier regression result for squared data

Price = 3.06279442 x size2 + 8.08258E-11 x resolution2 + 82.6009 x type2 -341.652964

 C B A D 1.03333 1 1.00107629 892.9103893

Table 7. Logaritmic regression result for squared data

ln(Price) = (size2 x ln(1.00107629)) + (resolution2 x ln(1)) + (type2 x ln(1.03333))+ ln(892.9103893)

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:

1. Price = 175.334352 x size + 0.000337169 x resolution + 398.949 x type -3592.12272

R2= 0.890255431

1. ln(Price) = (size x ln(1.06418144)) + (resolution x ln(1.000000081)) + (type x ln(1.17545))+ ln(279.7372771)

R2= 0.925487614

1. Price = 3.06279442 x size2 + 8.08258E-11 x resolution2 + 82.6009 x type2 -341.652964

R2= 0.869359579

1. ln(Price) = (size2 x ln(1.00107629)) + (resolution2 x ln(1)) + (type2 x ln(1.03333))+ ln(892.9103893)

R2= 0.907055222

Selection of Preferred Alternatives

As per the information above, the closer the R2 value to 1 is the second formula which is:

ln(Price) = (size x ln(1.06418144)) + (resolution x ln(1.000000081)) + (type x ln(1.17545))+ ln(279.7372771)

With this formula I could estimate how much a Toshiba, flat panel, small size television cost is.

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.

Toshiba television data and prices. (September 6, 2013). Retrieved from glodokshop.com

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

1 Comment

Filed under Sadat SD, Week 02

One response to “W2_SSD_Estimated Cost of a Television”

1. drpdg

Pagi Pak Sadat…… Hmmmm……… Interesting case study and you did a good job on your calculations but this was the wrong or inappropriate tool to use for this case study……. So I have little choice but to REJECT your posting …..

IF you were using the 20-22″ actual prices to predict what a 30-32″ screen would cost, then it might have made more sense but to convert known prices into a cost estimating model and then not project or extrapolate them doesn’t make much sense.

I am going to reject this posting and suggest that if you still want to use this case study (which is a good one) that you would be better off to do to a life cycle cost analysis as that is more appropriate to the case study you have selected.

OR if you want to create a cost estimating model, then what you would need to do is take the prices for a variety of different brands and sizes and see what the “best fit” line is to predict the cost of ANY TV based on size of the screen……

Here is what I would suggest for what would be an excellent posting. Plot the costs of a broad selection of different brands and different sizes compared against their costs. THEN look for the brand and size which offers the “best value” compared against your cost estimating model. In other words, what you are looking for is the outlier on the down side- that brand and size which offers the lowest price for the size. Does that make sense?

Repost as your W2.1_SSD_Topic……

BR,
Dr. PDG, Jakarta