(a) How many observations do you have in the data set? (b) Write down the corresponding regression model (c) Write down the estimated model (d) What's the R square and what does it mean? (e) Suppose you wanted to test whether the 'slopes' are jointly signifi- cantly different than zero? Write down the null hypothesis and the alternative hypothesis. At significance level of 1 per-cent, what do you conclude? (f) What is the estimated effect on sales from increasing the quality level by one unit, while holding fix advertisement investments? (g) What is the estimated effect on sales from decreasing advertisement investments by 2 units (that is 2k AUD). while holding fix quality level? (h) What are the estimated sales revenues of a firm that has quality level 0 and does not invest anything into advertisement? (i) What is the 95 per cent confidence interval of the coefficient estimator of quality level? I (i) Suppose you wanted to test whether investment in advertisement affects sales? What would be the null hypothesis, the test statistic. what would you conclude at the 1 per cent significance level?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Question
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2. Suppose you collect data on the quality level (measured on a continuous
some scale between 0 and 100, where 0 corresponds to the lowest quality
level and 100 to the highest quality level) of firms' product, on firms'
advertisement investments (measured in 1k AUD), and on firms' sales
revenues (measured in 1k AUD). You regress sales revenue on quality
level and on advertisement investments. Here is the Excel output:
SUMMARY OUTPUT
Multiple R
R Square
Regression Statistics
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
Advertisement Investments
Quality Level
0.999485812
0.998971888
0.998878423
1.808545855
df
25
2
22
F
SS
MS
69918.90249 34959.45124 10688 22426
71.95843842 3.27083811
24 69990.86093
Significance F
1.35658E-33
Coefficients Standard Error t Stat
Lower 95%
Upper 95%
P-value
13.7623304 17.17587708 0.801259251 0.431550907 21.8582585 49.3829193
1.450441963 0.434670743 3.33687506 0.00298855 0.548990015 2.35189391
4.963522727 0.034878648 142.308346 4.13434E-34 4.891188838 5.035856616
Transcribed Image Text:2. Suppose you collect data on the quality level (measured on a continuous some scale between 0 and 100, where 0 corresponds to the lowest quality level and 100 to the highest quality level) of firms' product, on firms' advertisement investments (measured in 1k AUD), and on firms' sales revenues (measured in 1k AUD). You regress sales revenue on quality level and on advertisement investments. Here is the Excel output: SUMMARY OUTPUT Multiple R R Square Regression Statistics Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Advertisement Investments Quality Level 0.999485812 0.998971888 0.998878423 1.808545855 df 25 2 22 F SS MS 69918.90249 34959.45124 10688 22426 71.95843842 3.27083811 24 69990.86093 Significance F 1.35658E-33 Coefficients Standard Error t Stat Lower 95% Upper 95% P-value 13.7623304 17.17587708 0.801259251 0.431550907 21.8582585 49.3829193 1.450441963 0.434670743 3.33687506 0.00298855 0.548990015 2.35189391 4.963522727 0.034878648 142.308346 4.13434E-34 4.891188838 5.035856616
(a) How many observations do you have in the data set?
(b) Write down the corresponding regression model
(c) Write down the estimated model
(d) What's the R square and what does it mean?
(e) Suppose you wanted to test whether the 'slopes' are jointly signifi-
cantly different than zero? Write down the null hypothesis and the
alternative hypothesis. At significance level of 1 per-cent, what do
you conclude?
(f) What is the estimated effect on sales from increasing the quality level
by one unit, while holding fix advertisement investments?
(g) What is the estimated effect on sales from decreasing advertisement
investments by 2 units (that is 2k AUD). while holding fix quality
level?
(h) What are the estimated sales revenues of a firm that has quality level
0 and does not invest anything into advertisement?
(i) What is the 95 per cent confidence interval of the coefficient estimator
of quality level?
I
(i) Suppose you wanted to test whether investment in advertisement
affects sales? What would be the null hypothesis, the test statistic.
what would you conclude at the 1 per cent significance level?
Transcribed Image Text:(a) How many observations do you have in the data set? (b) Write down the corresponding regression model (c) Write down the estimated model (d) What's the R square and what does it mean? (e) Suppose you wanted to test whether the 'slopes' are jointly signifi- cantly different than zero? Write down the null hypothesis and the alternative hypothesis. At significance level of 1 per-cent, what do you conclude? (f) What is the estimated effect on sales from increasing the quality level by one unit, while holding fix advertisement investments? (g) What is the estimated effect on sales from decreasing advertisement investments by 2 units (that is 2k AUD). while holding fix quality level? (h) What are the estimated sales revenues of a firm that has quality level 0 and does not invest anything into advertisement? (i) What is the 95 per cent confidence interval of the coefficient estimator of quality level? I (i) Suppose you wanted to test whether investment in advertisement affects sales? What would be the null hypothesis, the test statistic. what would you conclude at the 1 per cent significance level?
Expert Solution
Step 1: Given Information

The results of the regression of sales revenue on quality level and advertisement investments are given as

TABLE 1 

Regression Statistics
Multiple R0.999485812
R Square0.998971888
Adjusted R Square0.998878423
Standard Error1.808545855
Observations25

TABLE 2

ANOVA RESULTS

dfSSMSFSignificance F
Regression269918.9024934959.4512410688. 224261.35658E - 33
Residual2271.958438423.27083811

Total2469990.86093


TABLE 3


CoefficientsStandard Errort-StatP - valueLower 95 %Upper 95 %
Intercept13.762330417.175877080.8012592510.43155090721.858258549.3829193
Advertisement Investments1.4504419630.4346707433.336875060.002988550.5489900152.35189391
Quality Level4.9635227270.034878648142.3083464.13434E - 344.8911888385.035856616


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