Question

1)

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 ($)	40,000	50,000	50,000	60,000	70,000	70,000	80,000	80,000	90,000	100,000
Sales ($)	239,000	315,000	311,000	363,000	432,000	438,000	493,000	486,000	535,000	603,000

What is the slope of the "least-squares" best-fit regression line?

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.

2)

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 ($)	100,000	110,000	110,000	120,000	130,000	130,000	140,000	150,000	150,000	160,000
Sales ($)	603,000	676,000	655,000	748,000	796,000	785,000	858,000	891,000	935,000	980,000

What is the predicted sales quantity for an advertising budget of $136,000?

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.

3)

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 correlation 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

1:

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.997928258
R Square	0.995860807
Adjusted R Square	0.995343408
Standard Error	7739.145747
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.15281E+11	1.15281E+11	1924.74404	8.03972E-11
Residual	8	479155015.2	59894376.9
Total	9	1.15761E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	13057.75076	9626.179767	1.356483161	0.21198356	-9140.259571	35255.76109
Advertising ($), X	5.919452888	0.134925823	43.87190491	8.0397E-11	5.608313381	6.230592394

The slope of the regression line is 5.92

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2:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.994149561
R Square	0.98833335
Adjusted R Square	0.986875018
Standard Error	14283.17289
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.3826E+11	1.3826E+11	677.7152427	5.08955E-09
Residual	8	1632072222	204009027.8
Total	9	1.39892E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-12938.88889	31274.7494	-0.413716789	0.68995004	-85058.59027	59180.81249
Advertising ($), X	6.197222222	0.238052881	26.03296454	5.08955E-09	5.648271294	6.746173151

The regression equation is:

y' = -12938.89 + 6.1972x

The predicted value for X = 136,000 is

y' = -12938.89 + 6.1972 * 136000 = 829880.31

Answer: $829880

3)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.997458987
R Square	0.994924431
Adjusted R Square	0.994289985
Standard Error	8743.381685
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.19882E+11	1.19882E+11	1568.178086	1.81836E-10
Residual	8	611573786.4	76446723.3
Total	9	1.20494E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8090.035714	12085.85315	0.669380607	0.52209837	-19779.9916	35960.06303
Advertising ($), X	5.973205952	0.150837664	39.60022836	1.81836E-10	5.625373675	6.32103823

The  correlation value for the relationship between advertising and sales is

r = 0.9975

Answer: 1.00