A company conducts a survey to investigate the relationship between the monthly salary (X) and the amount of money spent on traveling in a year (Y). The results of 10 participants are recorded in the table below: X Monthly salary ($1,000) Y Amount of money spent on travelingin a year ($1,000) 9 3 12 8 35 21 42 61 30 40 22 20 14 15 18 11 33 17 19 25 (a) Calculate the coefficient of correlation of the above data. (b) Comment on the relationship between the monthly salary and the amount of money spent on traveling in a year by referring to your answer in part (a). (c) Find the values of a and b in the regression line y = a + bx of the above data.
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 company conducts a survey to investigate the relationship between the monthly salary (X) and the amount of money spent on traveling in a year (Y). The results of 10 participants are recorded in the table below:
| X Monthly salary ($1,000) |
Y Amount of money spent on travelingin a year ($1,000) |
| 9 | 3 |
| 12 | 8 |
| 35 | 21 |
| 42 | 61 |
| 30 | 40 |
| 22 | 20 |
| 14 | 15 |
| 18 | 11 |
| 33 | 17 |
| 19 | 25 |
(a) Calculate the coefficient of
(b) Comment on the relationship between the monthly salary and the amount of money spent on traveling in a year by referring to your answer in part (a).
(c) Find the values of a and b in the regression line y = a + bx of the above data.
(d) Interpret the value of b in the regression line in part (c).
(e) Use the regression line in part (c) to estimate the amount of money spends on traveling in a year of a person whose monthly salary is $10,000 per month.
(f) Comment on the reliability of the estimation in part (e) with reason.
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