Understanding statistics is essential to understand research in the social and behavioural sciences. In this course, you will learn the basics of statistics and how it is being applied in various fields. This course will also prepare you for the next course which is Inferential Statistics. You will learn methods of descriptive statistics. You will learn what variables are and how to organize and present data in an effective way.
Menu
▼
Ahad, 31 Mac 2019
linear relationship
Review
If the plot of n pairs of data (x , y) for an experiment appear to indicate a "linear relationship" between y and x, then the method of least squares may be used to write a linear relationship between x and y.The least squares regression line is the line that minimizes the sum of the squares (d1 + d2 + d3 + d4) of the vertical deviation from each data point to the line (see figure below as an example of 4 points).
The least square regression line for the set of n data points is given by the equation of a line in slope intercept form:
where a and b are given by
Problem 1
Consider the following set of points: {(-2 , -1) , (1 , 1) , (3 , 2)}
a) Find the least square regression line for the given data points.
b) Plot the given points and the regression line in the same rectangular system of axes.Problem 2
a) Find the least square regression line for the following set of data
b) Plot the given points and the regression line in the same rectangular system of axes.Problem 3
The values of y and their corresponding values of y are shown in the table belowx 0 1 2 3 4 y 2 3 5 4 6
a) Find the least square regression line y = a x + b.
b) Estimate the value of y when x = 10.Problem 4
The sales of a company (in million dollars) for each year are shown in the table below.x (year) 2005 2006 2007 2008 2009 y (sales) 12 19 29 37 45
b) Use the least squares regression line as a model to estimate the sales of the company in 2012.