An online market evaluation company e-Serve collects data and provides analytic solutions for sales promotion. A subsample of e-Serve for promotion expenditure and sales of several ecommerce businesses in million taka are provided below. Promotion 22 15 4 4 7 10 12 15 17 15 Sales 150 100 80 100 90 120 110 120 130 140 (a) Show that a simple linear regression model can be fitted with these variables and state a linear model for these variables. How the least square method is used to estimate parameters in a linear regression model? (b) At 5% level of significance test the hypothesis that the correlation is not positive. Based on the test result comment on the sign of the regression coefficient. (c) Find the regression line of sales on promotion expenditure by estimating parameters. Also, test the significance of slope coefficient at 5% level. (d) Find the 95% confidence interval for the mean sales with promotion expenditure of 7 million taka and comment on your results.
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.
An online market evaluation company e-Serve collects data and provides analytic solutions for sales promotion. A subsample of e-Serve for promotion expenditure and sales of several ecommerce businesses in million taka are provided below.
Promotion 22 15 4 4 7 10 12 15 17 15
Sales 150 100 80 100 90 120 110 120 130 140
(a) Show that a simple linear regression model can be fitted with these variables and state a linear model for these variables. How the least square method is used to estimate parameters in a linear regression model?
(b) At 5% level of significance test the hypothesis that the
(c) Find the regression line of sales on promotion expenditure by estimating parameters. Also, test the significance of slope coefficient at 5% level.
(d) Find the 95% confidence interval for the mean sales with promotion expenditure of 7 million taka and comment on your results.
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