Question

Check my work 4 Click here for the Excel Data File Actual series are plotted along with the superimposed linear and exponential trends. 25 8.33 points 20 eBook 15 Hint 10 Print -Linear (y) Expon. (y) References 5 0 t 0 5 10 15 20 25 b-1. Estimate a linear trend model and an exponential trend model for the sample. (Round your answers to 2 decimal places.) Variable Linear Trend Exponential Trend Intercept t Standard Error

Answer 1

We will be using excel to solve this problem.

Please find below attached images for clearly explained solution for this problem.

1)

casonate Pog Path :- Insert > Scatter - [simple Theo Right click on any of point on this plot Goto Add Trendline" ist select linear (check Box) at bottom select Display equation on chart Display R-squared value on chart (check both boxes) follow the same for process "Exponential Trend" je Repeat © with exponential" & After this we will calculate the estimated values for both lincar and exponential trend

In the below scatter plot we have displayed the equation and R² value as well.

Hence from R² we will be getting the exponential trend as a good fit for the given data.

Scatter Plot y = 0.7889x + 1.0948 R2 = 0.8923 25 y = 3.2005e0.0892X 20 R2 = 0.9162 15 LO у Linear (y) Expon. (y) 5 O 1 0 5 10 15 20 25 t

# Below is the detail theory of how to calculate MSE and MAD for the given data.

Page # To calculate MSE and MAD s MSE( Mean Squared Error) and MADC Mean Absolute Deviation) formula : MSE Ely; -ý;)² MAD = Ily; - ;; } h-) where y is actual value is forecasted value & Note :- We will do calculation using 75- Excel. Please find attached attached screen shot CD # Hence final table is linear tread Variable Intercept @ slope Ostandard error 1.09 0.79 Exponential trend 3.20 o og VITSE = 1.34. MISE : 1:62 (62) linear Trend Exponential Trend MSE MAD 2.63 1.35 1.80 1.13

Date Page 163 of both linear that :- By comparing the MSE and MAD Values and Exponential we can Exponential method perform better. say Because MSE (exponential) < msk (linear) and also MAD ( exponential) < MAD (linear)

Below is the screen shot of the excel workout.

To get the modulus value in calculation of MAD, use command "=abs(value1-value2)"

А B с D E F G H 1 t 2 1 3 2 4 3 5 4 6 5 7 6 8 7 9 8 9 10 11 10 y y = 0.7889x + 1.0948 y = 3.2005e 20.08922 for MSE(linear) for MSE(Exp) for MAD(linear) for MAD(Exp) 4.44 1.8837 3.499104391 6.53466969 0.885284546 2.5563 0.940895609 3.17 2.6726 3.825568362 0.24740676 0.429769877 0.4974 0.655568362 4.6 3.4615 4.18249119 1.29618225 0.174313606 1.1385 0.41750881 4.98 4.2504 4.572714667 0.53231616 0.165881342 0.7296 0.407285333 3.53 5.0393 4.999345719 2.27798649 2.158976841 1.5093 1.469345719 6.57 5.8282 5.465781146 0.55026724 1.219299277 0.7418 1.104218854 5.43 6.6171 5.97573467 1.40920641 0.29782633 1.1871 0.54573467 6.88 7.406 6.533266498 0.276676 0.120224121 0.526 0.346733502 6.21 8.1949 7.142815652 3.93982801 0.87014504 1.9849 0.932815652 7.17 8.9838 7.809235312 3.28987044 0.408621783 1.8138 0.6392353121 7.17 9.7727 8.537831455 6.77404729 1.87096289 2.6027 1.367831455 10.76 10.5616 9.334405105 0.03936256 2.032320804 0.1984 1.425594895 10.69 11.3505 10.20529851 0.43626025 0.23493553 0.6605 0.484701486 13.48 12.1394 11.15744566 1.79720836 5.394258644 1.3406 2.322554336 14.2 12.9283 12.19842747 1.61722089 4.006292589 1.2717 2.001572529 15.23 13.7172 13.33653215 2.28856384 3.585220515 1.5128 1.893467854 11.91 14.5061 14.58082118 6.73973521 7.133285795 2.5961 2.670821184 14.7 15.295 15.94120151 0.354025 1.54058119 0.595 1.241201511 16.52 16.0839 17.42850436 0.19018321 0.825380176 0.4361 0.908504362 19.93 16.8728 19.05457152 9.34647184 0.766375023 3.0572 0.87542848 12 11 13 14 15 12 13 14 15 16 16 17 18 17 19 18 19 20 21 22 20 1.34779 1.132550996 23 24 2.628288837 1.795787154 Std.Error 1.621199814 1.340069832 To round off these values to the 2 digit use command "=round(value,2)" 25

Thank you !

All the best !!