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Regression Analysis & T-Test - Assignment Example

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In the paper “Regression Analysis & T-Test” the author analyzes various statistical outputs such as descriptive statistics, graphical summaries, boxplots and a t-test for equality of means in order to understand that one form of advertising is more effective than the other…
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Regression Analysis & T-Test
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Regression Analysis & T-Test
Part 1:
T-Test
Given the data on radio and newspaper adverts do you think that one form of advertising is more effective than the other? In order to support your answer produce various statistical outputs such as descriptive statistics, graphical summaries, boxplots and perform a t-test for equality of means. Explain and discuss the output and analysis and draw an appropriate conclusion.
Two-sample t-test of equality of means
Descriptive Statistics
Discussion of the output and analysis
The mean expenditure spent on radio advertisements is 7573 while the mean expenditure spent on newspaper advertisements is 8368. The boxplots further shows some difference in the mean expenditure between radio and newspaper expenditures. We performed a t-test for equality of means, we observe the p-value to be 0.046 (a value less than α=0.05), this leads us in rejecting the null hypothesis of equal mean between the expenditure on radio and that on the newspapers.
Conclusion
Based on the results shown above, it is evident that more money was spent on newspaper advertisements than was spent on radio advertisements. Since we rejected the null hypothesis, we conclude that indeed the expenditure made on radios was significantly different from that made on newspapers.
Part 2:
Simple Regression Analysis
Based on a thorough analysis of the data provided do you think that there is evidence to support the company’s current patterns of spending? That is, do you think either radio or newspaper adverts have a sufficient impact on income to justify the expense? What recommendations would you give regarding future spending? Once again, support these recommendations with appropriate statistical outputs such as correlation coefficients, fitted line plots and regression output and perform appropriate hypothesis tests. Explain and discuss the output and analysis and give appropriate advice.
SOLUTION
Correlations: Profit, Radio, News
Profit Radio
Radio 0.802
0.000
News -0.104 -0.125
0.497 0.415
Cell Contents: Pearson correlation
The correlations matrix shows that there is a strong positive relationship between profits and radio expenditures (that is, the higher the radio expenditures the higher the profits made); with a coefficient of 0.802, this shows indeed a strong positive relationship that exists between the two variables (profits and radio expenditure). The relationship between profits and newspapers expenditure is however negative; that is the higher the newspaper expenditures the lower the profits.
Regression Analysis: Profit versus Radio, News
The regression equation is
Profit = 64720 + 81.2 Radio - 0.38 News
Predictor Coef SE Coef T P
Constant 64720 110993 0.58 0.563
Radio 81.236 9.407 8.64 0.000
News -0.382 8.969 -0.04 0.966
S = 112378 R-Sq = 64.4% R-Sq(adj) = 62.7%
Analysis of Variance
Source DF SS MS F P
Regression 2 9.57860E+11 4.78930E+11 37.92 0.000
Residual Error 42 5.30414E+11 12628893067
Total 44 1.48827E+12
Source DF Seq SS
Radio 1 9.57837E+11
News 1 22879824
Unusual Observations
Obs Radio Profit Fit SE Fit Residual St Resid
5 3584 396660 353916 53050 42744 0.43 X
44 8718 1077445 768154 43348 309291 2.98R
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence
From the regression table above, we observe the value of R-squared to be 64.4%; this implies that 64.4% of variation in the profits (dependent variable) is entirely explained by the two independent variables (radio and newspaper advertisements). The p-value of the overall model is 0.000 (a value less than α=0.05), leading us to reject the null hypothesis thus concluding that the overall model is appropriate and fit and that the two independent variables have an impact on the profits made by the company.
The coefficient of radio is 81.2; this indicates that for any unit change in radio expenditure, the dependent variable (profits) changes by 81.2. That is to say, if radio expenditure increases by one unit then we would expect the profits to increase by 81.2 and vice versa. The coefficient for newspaper expenditure on the other hand is -0.38 implying that for any unit change (increase) in the newspaper expenditure, the dependent variable (profits) decreases by 0.38.
Conclusions
From the above analysis it is evident that radio advertisements play an important role in enhancing the company’s profits on the other hand, the newspaper adverts have a negative effect on the profits.
Recommendations
Based on the above conclusions it would be advisable for the company to put more focus on radio advertisements than on the newspaper advertisements as it seems that radio advertisements have more impact than the newspapers. Read More
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