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Q.5: (12 marks) [CLO 1, 2, 3] Khalid has established a large trading company to import mobile phones from Korea and sell in the MENA region. His sales data shows that there is a positive relationship between sales revenue and advertisement expenditure. He wants to forecast for revenues if the advertisement expenses are increased from current years AED 12 million to AED 15 million. There are number of ways to forecast such as moving average method, and ftting a curve by using regression equation. The company hires a researcher who collects the data from company records on sales and advertisement expenses for previous years. The raw data is given in the table below. Annual Sales Annual Advertisement Year (AED Million) 2012 2013 2014 Expense (AED Million) 21 23 24 7 8
2015 2016 2017 2018 23 25 12 27 13 The researcher formulates the following equation for estimation: where Y = Annual Sales (Million $) and X = Annual Advertisement Expenses (Million $) (a) Use the moving average method to forecast the revenues if the advertisement expenses are increased from AED 12 to 15 million Use Excel computer software to solve the problem (c) (b) (b) Develop a scatter diagram and show the forecast for revenue. Estimate the following regression equation by using the above data. le, what are the estimated value of β0 and β1 parameters? Forecast the sales if the advertisement expenses increase AED $18 million? Estimate the Coefficient of determination R2 (c) (d)
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Answer #1

as per company policies i am answering 4 parts only.

x y x^2 y^2 xy
5 21 25 441 105
7 23 49 529 161
8 24 64 576 192
8 23 64 529 184
9 22 81 484 198
12 25 144 625 300
13 27 169 729 351
sum x sum y sum x^2 sum y^2 sum xy n
62 165 596 3913 1491 7

b)
excel output:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.887113891 0.786971055 0.744365266 1.005169565 7 ANOVA as MS F Significance F Regression Residual Total 118.66245645 18.66246 18.470990.007731659 5 5.051829268 1.010366 6 23.71428571 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 17.981707321.354957079 13.27105 4.34E-05 14.49867926 21.46473537 14.49867926 21.46473537 0.631097561 0.146842385 4.297789 0.007732 0.253627195 1.008567927 0.253627195 1.008567927 Intercept

c)
scatter plot given below

scatterplot 30 T 25 20 15 10 0 6 8 10 12 14 0 4

d)
slope, b1=  
{n*sum(xy) - sum(x)*sum(y)} / {n*sum(x^2) - [sum(x)]^2 }  
{7*1491 - 62*165} / {7*596 - [62]^2 }  
0.6311  
  
intercept, bo=  
{sum(y)*sum(x^2) - sum(x)*sum(xy)} / {n*sum(X^2) - [sum(X)]^2}  
{165*596 - 62*1491} / {7*596 - [62]^2}  
18.0  
  
regression equation:  
y = bo + b1*x  
y = 17.9817 + 0.6311*x  

e)
when x=   18
yhat = 17.9817+0.6311*18
Yhat = 29

f)
corr coef, r =   
(n*sum(XY) - sum(X)*sum(Y)) / ( sqrt(n*sum(x^2)-[sum(x)]^2) * sqrt(n*sum(y^2)-[sum(y)]^2) )  
(7*1491-62*165) / ( sqrt(7*596-[62]^2) * sqrt(7*3913-[165]^2) )  
0.887113891  
  
coef of determination, R^2  
0.887113890631588^2  
0.787  

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