Quiz Unit 3. Find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region. 1. z<0.83 2. z>-1.0 3. z>-1.56. Chapter 3 Examining Relationships
Find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.
When are some situations when we might want to examine a relationship between two variables?
In this chapter we will deal with relationships and quantitative variables; the next chapter will deal with more categorical variables.
The response variable is our dependent variable (traditionally y)
Jim wants to know how the mean 2005 SAT Math and Verbal scores in the 50 states are related to each other. He doesn't think that either score explains or causes the other.
Julie looks at some data. She asks, “Can I predict a state's mean 2005 SAT Math score if I know its mean 2005 SAT Verbal score?”Explanatory or Response?
When we deal with cause and effect, there is always a definite response variable and explanatory variable.
But calling one variable response and one variable explanatory doesn't necessarily mean that one causes change in the other.Explanatory and Response Variables
To answer a statistical question of interest involving one or more data sets, proceed as follows.
Organize and examine the data. Answer the key questions.
Construct appropriate graphical displays.
Calculate relevant summary statistics
Look for overall patterns and deviations
When the overall pattern is regular, use a mathematical model to describe it.
Let's say we wanted to examine the relationship between the percent of a state's high school seniors who took the SAT exam in 2005 and the mean SAT Math score in state that year. A scatterplot is an effective way to graphically represent our data.
But first, what is the explanatory variable and what is the response variable in this situation?Scatterplots
The Mean SAT Math scores and percent of hish school seniors who take the test, by state, with the southern states highlighted.
Is the South different?Adding Categorical Data
Linear relations are important because, when we discuss the relationship between two quantitative variables, a straight line is a simple pattern that is quite common.
A strong linear relationship has points that lie close to a straight line.
A weak linear relationship has points that are widely scattered about a line.Measuring Linear Association:Correlation
Our eyes are not good measures of how strong a linear relationship is, so...
A numerical measure along with a graph gives the linear association an exact value.