Respuesta :
Answer:
The equation of the resulting line y = b₀ +b₁ x
The resulting line with intercept b₀ and slope b1 is called the least squares regression.
[tex]b_{1} = r \frac{s_{y} }{s_{x} }[/tex]
Step-by-step explanation:
Explanation:-
- In regression analysis, the variable that we are trying to describe or predict defines the vertical y-axis is called the response.
- The Association variable goes on the horizontal x-axis and is called the explanatory variable or predictor.
- Explanatory variables are Factors , covariates, or even independent variables.
- In regression analysis The symbol Y denotes the response and The symbol X denotes the explanatory variable
- For example diamonds cost depends on weight
- cost is the response and weight is the explanatory variable
Regression analysis can produce various types of equations. The most common equation is line. Before we fit a line ,we need to inspect the scatterplot of the data to see that Association between the Variables is linear.
- The equation of the resulting line y = b₀ +b₁ x
- Estimated cost = b₀ +b₁ weight
least squares
It remains to choose b₀ and b₁. unless every point lie on a single line( in which the correlation r=-1 and r=1)
we have to decide the best fit line to be close to the data, but the several ways to measure the distance from a point to a line .we could use horizontal distance, the perpendicular distance, or the vertical distance as sketched in graph.
- we choose to measure the distance of each data point to the line vertically because we use the fitted line to predict the value y from x. The vertical distance is called the error of prediction.
- The vertical deviations from the data points to the line are called residuals.
- The residue formula e = y-y⁻ = y - b₀ -b₁ x
The resulting line with intercept b₀ and slope b1 is called the
least squares regression.
[tex]b_{1} = r \frac{s_{y} }{s_{x} }[/tex]
