You have to study the relationship between the monthly e-commerce sales and the online advertising costs. You have the survey results for 7 online stores for the last year. Your task is to find the equation of the straight line that fits the data best. The following table represents the survey results from the 7 online stores. Store Monthly E-commerce Sales (in 1000 s) Online Advertising Dollars (1000 s) 1 368 1.5 2 340 1.3 3 665 2.8 4 954 0.8 5 331 1 6 556 2.2 7 376 1.3 (a) Find the correlation coefficient and interpret the result. Use a TI-84 and check the graph of the scatter plot. If you see any outlier(s), exclude them from the data set, then answer the following questions. (b) Find the correlation coefficient without outlier(s) and interpret the result. (c) Apply critical value test if there exists a linear relation. Show your work. Find the equation of the least square regression without outlier(s) and answer the following questions. (d) Find the slope and interpret. Round the slope to nearest thousandth. (e) Find the y-intercept and interpret if the value is reasonable. If the interpretation for the y-intercept is not reasonable, explain why. Round the y-intercept to nearest thousandth.
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.
You have to study the relationship between the monthly e-commerce sales and the online advertising costs. You have the survey results for 7 online stores for the last year.
Your task is to find the equation of the straight line that fits the data best.
The following table represents the survey results from the 7 online stores.
| Store | Monthly E-commerce Sales (in 1000 s) |
Online Advertising Dollars (1000 s) |
| 1 | 368 | 1.5 |
| 2 | 340 | 1.3 |
| 3 | 665 | 2.8 |
| 4 | 954 | 0.8 |
| 5 | 331 | 1 |
| 6 | 556 | 2.2 |
| 7 | 376 | 1.3 |
(a) Find the
Use a TI-84 and check the graph of the
(b) Find the correlation coefficient without outlier(s) and interpret the result.
(c) Apply critical value test if there exists a linear relation. Show your work.
Find the equation of the least square regression without outlier(s) and answer the following questions.
(d) Find the slope and interpret. Round the slope to nearest thousandth.
(e) Find the y-intercept and interpret if the value is reasonable. If the interpretation for the y-intercept is not reasonable, explain why. Round the y-intercept to nearest thousandth.
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