Reported below are the amounts spent on advertising ($ millions) by a large firm from 2007...

Reported below are the amounts spent on advertising ($ millions) by a large firm from 2007 to 2017. Year Amount 2007 94.2 2008 96.9 2009 108.2 2010 109.3 2011 118.3 2012 129.5 2013 141.0 2014 141.5 2015 152.1 2016 163.1 2017 165.7 Click here for the Excel Data File Determine the logarithmic trend equation. (Do not round your intermediate calculations. Round your answers to 4 decimal places.) Estimate the advertising expenses for 2022. (Do not round intermediate calculations. Round your answer to 2 decimal places.) By what percent per year did advertising expense increase during the period? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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Expert Solution

Amount( in $Mn)	Year(X)	Ln X	SUMMARY OUTPUT
94.2	2007	7.6044
96.9	2008	7.6049	Regression Statistics
108.2	2009	7.6054	Multiple R	0.993127536
109.3	2010	7.6059	R Square	0.986302303
118.3	2011	7.6064	Adjusted R Square	0.984780337
129.5	2012	7.6069	Standard Error	3.15021625
141.0	2013	7.6074	Observations	11
141.5	2014	7.6079
152.1	2015	7.6084	ANOVA
163.1	2016	7.6089		df	SS	MS	F	Significance F
165.7	2017	7.6094	Regression	1	6431.107056	6431.107056	648.0447615	1.07187E-09
			Residual	9	89.3147618	9.923862422
			Total	10	6520.421818
The Logarithm Trend equation of the line is Amount (Y) =Parameter estimate(b) * LnX + intercept(c) Amount (Y) = 15384.1591 * Ln X + -116896.4301 Amount (Y) = 15384.1591 * Ln X - 116896.4301
				Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
			Intercept	-116896.4301	4597.037249	-25.42864539	1.08243E-09	-127295.6508	-106497.2093	-127295.6508	-106497.2093
			Ln X	15384.15909	604.3259732	25.45672331	1.07187E-09	14017.07876	16751.23942	14017.07876	16751.23942



			RESIDUAL OUTPUT

			Amount( in $Mn)	Predicted Amount( in $Mn)	Residuals
			94.2	90.81313458	3.386865424
			96.9	98.47647674	-1.576476745
			108.2	106.1360035	2.063996542
			109.3	113.7917185	-4.491718514
			118.3	121.4436257	-3.143625703
			129.5	129.0917288	0.408271189
			141	136.7360316	4.26396838
			141.5	144.3765379	-2.876537904
			152.1	152.0132514	0.086748568
			163.1	159.646176	3.453824032
			165.7	167.2753153	-1.575315269

The parameter estimate and the intercept can also be calculated by using the formulas in the excel.

	Calculated value	Formula Used
c	15384.15909	c: =INDEX(LINEST(y,LN(x)),1)
b	-116896.4301	b: =INDEX(LINEST(y,LN(x)),1,2)

B. For 2022, the estimated advertising expenses is given by,

Amount (Y) = 15384.1591 * Ln X - 116896.4301

Amount (Y) = 15384.1591 * Ln 2022 - 116896.4301

Amount (Y) = 15384.1591 * 7.6118 - 116896.4301 = 205.3644

Therefore , Advertising expenses for 2022 is $ 205.36 Mn.

C. Advertising expenses in 2007 = 94.2

Advertising expenses in 2017 = 165.7

which means Advertising expenses have grown to 175.90% (= 165.7 / 94.2 ) of 2007 expenses in 2017

CAGR growth of Advertising expenses from 2007 to 2017 = (175.90%^(1/10) - 1 ) = 105.81% - 1 = 5.81%

Therefore, Advertising expenses have grown by 5.81% from 2007 to 2017.

orchestra answered 1 year ago

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