The multiple linear regression is an extension of simple linear regression analysis. However, Two problems arise due to multiple regressions.
i) State two problems that arise to the economic model and explain their impact
ii) Given a model Y = 27+ 9x + 12x. Where X1 = Capital Investment(000), and X2 = Market Expenditure (K000), and Y = Predicted Sales (k000)
Interpret the multiple linear regression model
i) Two problems that arise in multiple linear regression analysis are multicollinearity and heteroscedasticity.
- Multicollinearity occurs when there is a high correlation between two or more predictor variables in the model. This can make it difficult to determine the individual impact of each variable on the dependent variable. It can also lead to unstable coefficient estimates and a violation of the assumption of independent predictors. This problem may impact the economic model by making it challenging to identify the true relationship between the predictors and the predicted outcome accurately.
- Heteroscedasticity refers to the unequal variance of residuals across different levels of the predictor variables. In other words, the spread of the residuals is not constant. This violates the assumption of homoscedasticity, which assumes that the variability of the residuals is constant across all values of the predictors. Heteroscedasticity can affect the precision of coefficient estimates, lead to biased standard errors, and result in incorrect statistical inference. It may impact the economic model by compromising the reliability of the estimated effects of the predictor variables on the predicted sales.
ii) The given multiple linear regression model is: Y = 27 + 9x1 + 12x2, where Y represents the predicted sales in thousands, x1 represents the capital investment in thousands, and x2 represents the market expenditure in thousands.
Interpretation:
- The intercept term (27) represents the predicted sales when both the capital investment and market expenditure are equal to zero. In this case, it suggests that there is a base level of sales, even without any investment or expenditure.
- The coefficient of x1 (9) indicates that for each unit increase in capital investment (in thousands), the predicted sales are expected to increase by 9 units (in thousands), assuming all other factors remain constant.
- The coefficient of x2 (12) suggests that for each unit increase in market expenditure (in thousands), the predicted sales are expected to increase by 12 units (in thousands), assuming all other factors remain constant.
- It's important to note that interpreting the coefficients in a multiple regression model requires considering the assumptions of the model, potential interactions among predictor variables, and the context of the specific data and research question. Further analysis and diagnostics should be conducted to validate the model and interpret the results appropriately.