A Manager wants to know whether the level of Sale (Y) in Peshawar regions in 6 months after Advertisement could be predicted with strategy (X1) and (X2). (a)The least squares estimation equation involving both independent variables is given by Y = -0.628 + 23.639(X1) – 7.147(X2) Using this equation, determine the predicted level of Sale (Y) for Peshawar region with scores of 2.80 on Strategy X1 and 7.0 on Strategy X2. How does the predicted value obtained compare with the actual value of 25 observed for this region? (b)Using the analysis of variance tables below, carry out the overall F test for each of three models: i) model with X1 alone; ii) model with X2 alone; and iii) model with both X1 and X2 (c)Based on your results in part (b), how would you rate the importance of the two variables in predicting Y? (d)What are the R 2 values for the three regressions referred to in part (b)? (e)Based on the above, in your opinion, which is the best model involving either one or both of the two independent variables?

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.