Question

In: Statistics and Probability

1) Consider the following sample data for the relationship between advertising budget and sales for Product...

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 ($) 40,000 50,000 50,000 60,000 70,000 70,000 80,000 80,000 90,000 100,000
Sales ($) 240,000 308,000 315,000 358,000 425,000 440,000 499,000 494,000 536,000 604,000

What is the predicted sales quantity for an advertising budget of $68,000?

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.

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 ($) 50,000 60,000 60,000 70,000 70,000 80,000 90,000 90,000 100,000 110,000
Sales ($) 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.

Solutions

Expert Solution

1) What is the predicted sales quantity for an advertising budget of $68,000?

We know regression equation is,

Y = a + b*X.

Here, X : Independent variable = Advertising and Y : Dependent variable = Sales

By using Excel data analysis tool, we calculate regression.

Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.9971322
R Square 0.9942727
Adjusted R Square 0.9935567
Standard Error 9239.0163
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 1.185E+11 1.185E+11 1388.8101 2.94894E-10
Residual 8 682875380 85359422
Total 9 1.192E+11
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7711.25 11491.76 0.67 0.52 -18788.81 34211.30
Advertising ($) 6.00 0.16 37.27 0.00 5.63 6.37

Therefore, Regression equation is,

Sales = 7711.25 + 6.00 * Advertising.

Then,

Sales = 7711.25 + 6.00 *.68000

= 415897

The predicted sales quantity for an advertising budget of $68,000 is $415,897.

2) What is the correlation value for the relationship between advertising and sales?

By using Excel data analysis tool, we calculate correlation.

Output:

Advertising ($) Sales ($)
Advertising ($) 1
Sales ($) 0.997 1

The correlation value for the relationship between advertising and sales is 0.997


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