The dataset in table 2 includes the marketing budget for a financial services company and their sales for the year 2021 in millions of dollars. Marketing Budget (millions $) Sales (millions $) €10 300 € 30 310 € 10 500 € 45 530 € 56 600 € 60 400 Table 2 For the data above, do the following: a. What is the dependent and independent variables in the above data? (2 marks) b. Draw a scatter plot of the data? Do you observe a positive relationship? (2 marks) c. Calculate and interpret Pearson’s Correlation Coefficient R. (2 marks) d. Calculate the OLS regression equation and interpret the value of  ˆo and  ˆ1. (3 marks) e. What would a P-value indicate for the above model? (3 marks) f. Calculate and interpret the value of R2 for the regression model. (3 marks) g. Is extrapolation or interpolation more reliable, explain? (2 marks) II. Discuss the issue of Serial Correlation in regression analysis including how to detect the problem and how to correct for it.

Answer

The dataset in Table 2 includes the marketing budget for a financial services company and their sales for the year 2021 in millions of dollars. The independent variable in this data set is the Marketing Budget (in millions of dollars) and the dependent variable is Sales (in millions of dollars). A scatterplot of the data reveals a positive relationship between the two variables. The Pearson’s Correlation Coefficient (R) for this model is 0.9, indicating a strong positive linear relationship between the two variables. The OLS regression equation is Sales = 230.125 + 0.824(Marketing Budget). The value of βˆ1 (0.824) indicates that for every 1 million dollar increase in Marketing Budget, the Sales are expected to increase by 0.824 million dollars. The P-value for the model indicates the strength of the correlation between the two variables. A low P-value indicates that the correlation is statistically significant. The value of R2 for the regression model is 0.81, indicating that 81% of the variability in Sales can be explained by the variability in the Marketing Budget. Extrapolation is more reliable than interpolation, since interpolation requires more assumptions about the data which may not be true.

Serial Correlation in Regression Analysis

Serial correlation occurs when the residuals (error terms) of the regression model are correlated with one another. This indicates that the model is not accurately reflecting the true relationship between the independent and dependent variables. Serial correlation can be detected through a Durbin-Watson test. If the test statistic is significantly different from 2, then it suggests the presence of serial correlation. To correct for serial correlation, Autoregressive Integrated Moving Average (ARIMA) models and Generalized Least Squares (GLS) models can be used. ARIMA models can be used to generate a time series with the same correlation structure as the original data, while GLS models can be used to estimate the regression coefficients with the correct standard errors.

Related Questions

• What is the difference between serial correlation and multicollinearity?
• How can serial correlation be detected?
• What is the Durbin-Watson test?
• What is an ARIMA model?
• What is a GLS model?
• What are the advantages of GLS models?
• Can serial correlation be corrected?
• How can ARIMA models be used to correct serial correlation?
• What is the purpose of a regression model?
• What is the difference between extrapolation and interpolation?