A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). yy^=a+bx a=-1.218 b=0.171 (b) Which is a possible value for the correlation coefficient, r? (c) If a country increases its life expectancy, the happiness index will increase or decrease ? (d) If the life expectancy is increased by 5 years in a certain country, how much will the happiness index change? Round
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 regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).
yy^=a+bx
a=-1.218
b=0.171
(b) Which is a possible value for the
(c) If a country increases its life expectancy, the happiness index will
increase or decrease ?
(d) If the life expectancy is increased by 5 years in a certain country, how much will the happiness index change? Round to two decimal places.
(e) Use the regression line to predict the happiness index of a country with a life expectancy of 59 years. Round to two decimal places.
Note:
As per the guidelines, we are only allowed to solve three subparts, please post the other questions as a different question.
The general form of the regression line is:
Where ′Y^ is the predicted value, 'a' is the intercept, 'b' is the slope of the line and 'X' is the independent variable.
In this case, the regression line is given as:
The slope of this equation is 0.171.
Since the slope of the regression line is positive, thus if the value of X increases, the value of Y^ increases. Therefore, it can be concluded that for every one-unit increase in x, there is a 0.171 increase in y.
(a)
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