The manager of a car dealership wants to predict the relationship between number of sales persons and the number of cars sold. He collects some data to develop a regression model, which is given below Week Number of cars sold Number of salespersons 1 80 6 2 90 8 3 48 4 4 55 5 5 60 7 6 75 9 7 100 11 8 70 6 9 65 7 10 98 10 (i) Run a regression analysis which explains the number of cars sold in terms of number of salespersons, and estimate the regression line (ii) Interpret the regression coefficient, and determine the significance of the regression coefficient. (iii) Interpret the overall model fit (iv) What would be the number of cars sold if company deploys 15 salespersons
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.
The manager of a car dealership wants to predict the relationship between number of sales persons and the number of cars sold. He collects some data to develop a regression model, which is given below
|
Week |
Number of cars sold |
Number of salespersons |
|
1 |
80 |
6 |
|
2 |
90 |
8 |
|
3 |
48 |
4 |
|
4 |
55 |
5 |
|
5 |
60 |
7 |
|
6 |
75 |
9 |
|
7 |
100 |
11 |
|
8 |
70 |
6 |
|
9 |
65 |
7 |
|
10 |
98 |
10 |
(i) Run a
(ii) Interpret the regression coefficient, and determine the significance of the regression coefficient.
(iii) Interpret the overall model fit
(iv) What would be the number of cars sold if company deploys 15 salespersons
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