A sales manager has collected the following data on annual sales (y) and years of experience (x) . Sales person Years of Experience (x) Annual Sales (K’000) (y) 1 80 3 97 4 92 4 102 6 103 6 8 111 10 119 10 123 11 117 13 136 Draw a scatter diagram. Does a linear relationship between x and y seem appropriate Estimate the simple linear regression line. Interpret the parameters in the model (c) What practical use could be made of this equation? Use the estimated regression equation to predict annual sales for a sales man with 9 years of experience
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.
A sales manager has collected the following data on annual sales (y) and years of experience (x)
.
Sales person Years of Experience (x) Annual Sales (K’000) (y)
- 1 80
- 3 97
- 4 92
- 4 102
- 6 103 6 8 111
- 10 119
- 10 123
- 11 117
- 13 136
- Draw a
scatter diagram . Does a linear relationship between x and y seem appropriate - Estimate the simple linear regression line. Interpret the parameters in the model (c) What practical use could be made of this equation?
- Use the estimated regression equation to predict annual sales for a sales man with 9 years
of experience
- At the 5% level of significance would you conclude that there is a linear relationship between x and y ?
- Construct a 95% confidence interval for the slope parameterβ1.
- Find the
correlation coefficient (h)Find the coefficient of determination and interpret the value. - Give the ANOVA table
Use the ANOVA table to test for a significant linear relationship between years of experience and annual sales
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