Below are the average heights for American boys in 1990. Age (years) Height (cm) birth 50.8 2 83.8 3 91.4 5 106.6 7 119.3 10 137.1 14 157.5 Part 1) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.) ŷ =_________+___________ x Part 2) Use the least squares line to estimate the average height for a sixty-five-year-old man. (Use your equation from part (1). Round your answer to one decimal place.) ___________ cm Part 3) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.) Interpret the slope. (Round your answer to three decimal places.) _______________ (slope) As age increases by one year, the average height (increases or decreases) by _______________ cm
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.
Below are the average heights for American boys in 1990.
| Age (years) | Height (cm) |
|---|---|
| birth | 50.8 |
| 2 | 83.8 |
| 3 | 91.4 |
| 5 | 106.6 |
| 7 | 119.3 |
| 10 | 137.1 |
| 14 | 157.5 |
Part 1) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.)
ŷ =_________+___________ x
Part 2) Use the least squares line to estimate the average height for a sixty-five-year-old man. (Use your equation from part (1). Round your answer to one decimal place.)
___________ cm
Part 3) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.) Interpret the slope. (Round your answer to three decimal places.)
_______________ (slope)
As age increases by one year, the average height (increases or decreases) by _______________ cm
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