Question

Consider the following sample data for the relationship between advertising budget and sales for Product A:

Observation	1	2	3	4	5	6	7	8	9	10
Advertising ($)	50,000	60,000	60,000	70,000	70,000	80,000	90,000	90,000	100,000	110,000
Sales ($)	299,001	371,000	364,000	430,000	440,000	485,000	535,000	546,000	595,000	675,000

What is the predicted sales quantity for an advertising budget of $76,000?

Please round your answer to the nearest integer.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Consider the following sample data for the relationship between advertising budget and sales for Product A:

Observation	1	2	3	4	5	6	7	8	9	10
Advertising ($)	40,000	40,000	50,000	60,000	60,000	60,000	70,000	80,000	80,000	90,000
Sales ($)	239,000	248,000	316,000	365,000	358,000	375,000	432,000	476,000	486,000	552,000

What is the R² coefficient of determination value for the relationship between advertising and sales?

Please round your answer to the nearest hundredth.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Answer 1

Consider the following sample data for the relationship between advertising budget and sales for Product A:

observation	advertising	sales
1	50000	299001
2	60000	371000
3	60000	364000
4	70000	430000
5	70000	440000
6	80000	485000
7	90000	535000
8	90000	546000
9	100000	595000
10	110000	675000

What is the predicted sales quantity for an advertising budget of $76,000?

Solution:

Using excel<data<megastat<correlation/regression<regression<select type predicted value as 76000

Here is the output:

Regression Analysis
	r²	0.995
	r	0.997
	Std. Error	8743.382
	n	10
	k	1
	Dep. Var.	sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,19,88,20,76,214.5190	1	1,19,88,20,76,214.5190	1568.18	1.82E-10
Residual	61,15,73,786.3810	8	7,64,46,723.2976
Total	1,20,49,36,50,000.9000	9
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	8,090.0357
advertising	5.9732	0.1508	39.600	1.82E-10	5.6254	6.3210
Predicted values for: sales
		95% Confidence Interval	95% Prediction Interval
advertising	Predicted	lower	upper	lower	upper	Leverage
76,000	4,62,053.688	4,55,639.978	4,68,467.398	4,40,895.877	4,83,211.500	0.101

The answer is Sales is predicted to be $462,054 with an advertising budget of $76,000.

........................................................................................................................................................................................

observation	advertising	sales
1	40000	239000
2	40000	248000
3	50000	316000
4	60000	365000
5	60000	358000
6	60000	375000
7	70000	432000
8	80000	476000
9	80000	486000
10	90000	552000

Using excel<data<megastat<correlation/regression

Regression Analysis
	r²	0.995
	r	0.998
	Std. Error	7631.855
	n	10
	k	1
	Dep. Var.	sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	94,18,81,38,314.1762	1	94,18,81,38,314.1762	1617.10	1.61E-10
Residual	46,59,61,685.8238	8	5,82,45,210.7280
Total	94,65,41,00,000.0000	9
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	6,241.3793
advertising	6.0073	0.1494	40.213	1.61E-10	5.6628	6.3518

The R2= 1 coefficient of determination value for the relationship between advertising and sales

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