Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit. Use a significance level of 0.01 and round all values to 4 decimal places. Advertising Cost Profit 3 21 4 22 18 6. 23 7 30 8. 33 9 23 10 31 Ho: p = 0 Ha: p #0 Find the Linear Correlation Coefficient Find the p-value p-value The p-value is O Less than (or equal to) a O Greater than a The p-value leads to a decișion to O Reject Ho O Accept Ho Do Not Reject Ho The conclusion is O There is a significant positive linear correlation between advertising expense and profit. O There is a significant negative linear correlation between advertising expense and profit. There iea rianifiennt lineareOrralation between aduartivaine nence and neofit
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.
Given the data;
| Advertising cost(X) | profit(Y) | XY | X2 | Y2 |
| 3 | 21 | 63 | 9 | 441 |
| 4 | 22 | 88 | 16 | 484 |
| 5 | 18 | 90 | 25 | 324 |
| 6 | 23 | 138 | 36 | 529 |
| 7 | 30 | 210 | 49 | 900 |
| 8 | 33 | 264 | 64 | 1089 |
| 9 | 23 | 207 | 81 | 529 |
| 10 | 31 | 310 | 100 | 961 |
| 52 | 201 | 1370 | 380 | 5257 |
Correlation coefficient is given by-
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