*margin of error= measure of accuracy of a sample population
-the amount by which the sample proportion differs from the true population proportion is less than this quantity in at least 95% of all random samples.
usually reported in percentages (x 100)
Sample Size & Margin of Error
You can gauge the opinion of millions in a brief sample of 1500 by within 3%
Positively Associated Variables
*When the values of one variable tends to increase as the value of the other variable increases
EX: tall people and hand size
Negatively Associated Variables
*When the values of one variable tend to decrease as the values of the other variable increase
When the relationship pattern of two variables resembles a straight line
When a curve describes the pattern of a scatterplot better than a line does
*used to examine relationship between a quantitative response variable and one of more explanatory variables
Describes how, on average, the response variable is related to explanatory variables
*can predict response variable using known values of explanatory variable EX: equation between verbal SAT score and college GPA. Could use the equation to PREDICT potential GPA's of students.
A straight line that describes how values of a quantitative response variable (y) are related on average, to values of quantitative explanatory variable (x)
*THE LINE IS USED FOR: 1. estimating the average value of y at any specified value of x 2. predicting the value of y for an individual, given that individual's x value
Equation of a Straight Line
relating to y and x is:
y=b0 + b1x
b0= y intercept b1=slope
Handspan= -3 +0.35 (Height)
Interpreting the Slope
Measures how much the y variable changes per each one-unit increase in the value of the x variable
Handspan= -3 +0.35 (Height) **THIS means that handspan increases by .35 cm on average for each 1 in increase in height. we can estimate avg. diff in handspan bc if heights differ by 7 inches do [7 x .35= 2.45 cm] difference in handspans is approx 1 i.
difference between observed y-value and predicted y-value (y-yhat)
the more neutral term for the difference between (y-yhat) [observed y value - predicted y-value]
Basis for estimating equation of regression line "least sum of squared errors"
between two quantitative variables, this is the number that indicates strength and direction of a straight-line relationship
the strength of the relationship is determined by the closeness of the points to a straight line
the direction is determined by whether one variable generally increases or decreases when the other variable increases
represented by "r"
measures sometimes called "correlation coefficient"
doesn't matter which variable is x and which is y
Correlation coefficients always between -1 and +1
a correlation of -1 or +1 indicates a perfect linear relationship and all data points fall on the same straight line
correlation of 0 indicates that the best straight line thru data is horizontal
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