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In Business Mathematics and Statistics, statistical methods are widely used to study the relationship between two variables and to make estimates for future business decisions. In the present problem, advertising expenditure is considered the independent variable, while sales are considered the dependent variable. The objective is to estimate the expected sales when the advertising expenditure is ₹7 lakh. Such an estimation is generally made with the help of regression analysis, particularly the regression equation of sales on advertising expenditure. Advertising expenditure and sales are usually positively related. When a firm increases its expenditure on advertising, it may reach more customers, improve brand awareness, increase demand and consequently increase sales. However, the exact increase in sales cannot be determined merely by observing the advertising expenditure. Statistical analysis is therefore used to establish the average relationship between the two variables. Let advertising expenditure be represented by (X), and sales by (Y). If observations relating to advertising expenditure and sales for different periods are available, a regression equation can be obtained in the form: [ Y=a+bX ] where (a) is the intercept and (b) is the regression coefficient of sales on advertising expenditure. The regression coefficient (b) indicates the expected change in sales corresponding to a one-unit change in advertising expenditure. Once the values of (a) and (b) are calculated from the given data, the regression equation can _____ _________ ____ _______ ________ _________ ______ ____ ______ _____ _____.
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