Regression analysis is a method of obtaining relationship among any two variables (Field, 2005). Twenty movies from 1999 and 2000 were listed together with their variables. Linear regression analysis was performed and graphs plotted in order to determine the relationship between the variables.
Plots showing variable relationships
Interpretation
Using r value and the p-value, it is clear that the best line of fit is significant at 0.05 significant level. This is because after calculating the p-value using Excel, the value obtained is 0.00020129. The p-value is less than the α level of significance, therefore, the null hypothesis of no difference is rejected and hence the alternative hypothesis accepted (Field, 2005).
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Confidence Interval
| Lower 95% | Upper 95% |
15.86308036 | 41.59239726 |
0.547551216 | 0.95603975 |
The confidence level is between 0.55 and 0.96. this implies that 0.55<0.88<0.96. Therefore, r is not significant and should not be used for prediction.
Interpretation
Using r value and the p-value, it is clear that the best line of fit is not significant at 0.05 significant level. This is because after calculating the p-value using Excel, the value obtained is 0.300180611. The p-value is greater than the α level of significance, therefore, the null hypothesis of no difference is not rejected.
Confidence Interval
| Lower 95% | Upper 95% |
-104.3100388 | 318.425293 |
-0.410538612 | 5.068131734 |
The confidence level is between 0.41 and 5.07. This implies 0.41<5.07< r. Therefore, r is significant and should be used for prediction
Interpretation
Using r value and the p-value, it is clear that the best line of fit is not significant at 0.05 significant level. This is because after calculating the p-value using Excel, the value obtained is 0.110594992. The p-value is greater than the α level of significance, therefore, the null hypothesis of no difference is not rejected
Interpretation
Using r value and the p-value, it is clear that the best line of fit is not significant at 0.05 significant level. This is because after calculating the p-value using Excel, the value obtained is 0.310469063. The p-value is greater than the α level of significance, therefore, the null hypothesis of no difference is not rejected
Report
Looking at the linear regression graph of tomatoemeter vs audience, it appears that the critics and the audience agree on what a movie should be rated. This is because there is a strong relationship between the independent and the dependent variable of .78. Furthermore, performing a hypothesis test results in a very low p-value (probability of making type I error) therefore the null hypothesis is rejected meaning there is sufficient reason to believe that both the critics and the audience agree on the same thing.
Large budgets do not necessarily lead to high grossing as observed from the tests above. Looking at the linear regression graph of budget vs gross, the r squared value is very low (.159) and this implies very weak correlation between the two variables. In fact, it implies that there is only 15.9% chance of correlation between the two sets of variables. The null hypothesis, in this case, was not rejected due to a large p-value, therefore large budgets do not contribute to large worldwide gross.
There is no relationship between higher ratings and higher budgets. This is due to a low r squared value in the graph showing the relationship between budget and ratings. The r squared value, in this case, is .143 which translates to a very weak relationship. The null hypothesis too is not rejected therefore supporting the claim of no difference. Lastly, higher ratings by audience members are not associated with higher gross amounts earned by the movie. The p-value obtained from this graph is larger than the .05 α level of significance, therefore, the null hypothesis is not rejected and this implies there is indeed no association between the two variables.
Conclusion
Without linear regression, it is difficult to tell which variables have an association from the ones that don’t. It is only after having performed regression analysis that one is able to tell that higher budgets do not necessarily lead to higher gross as people might expect. Linear regression, therefore, is the perfect tool for carrying out such simple statistical analyses.
Reference
Field, A. (2005). Discovering statistics using SPSS (2nd ed.). Thousand Oaks, CA: Sage Publication Ltd.
