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.
Here I shall answer the question by giving you the whole calculation which has been done in excel
So, first, we will start to with the data
| Observations | Advertising $ | Sales $ |
| 1 | 40000 | 239000 |
| 2 | 50000 | 315000 |
| 3 | 50000 | 311000 |
| 4 | 60000 | 363000 |
| 5 | 70000 | 432000 |
| 6 | 70000 | 438000 |
| 7 | 80000 | 493000 |
| 8 | 80000 | 486000 |
| 9 | 90000 | 535000 |
| 10 | 100000 | 603000 |
Now I have used the data analysis tool pack to find the regression equation.
the equation and another summary of the model is given below
| 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% | Lower 95.0% | Upper 95.0% | |
| Intercept | 13057.75076 | 9626.179767 | 1.356483161 | 0.211983555 | -9140.259571 | 35255.76109 | -9140.259571 | 35255.76109 |
| X Variable 1 | 5.919452888 | 0.134925823 | 43.87190491 | 8.03972E-11 | 5.608313381 | 6.230592394 | 5.608313381 | 6.230592394 |
From the above calculation, we can see that the slope will be 5.92 (two decimal place)
Hope this answer has helped you. If you have some queries regarding this, do let me know in the comment section.
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Consider the following sample data for the relationship between advertising budget and sales for Product A:...
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