HS STATS CH.3
A(n) _____ is a comparison of two values, usually x and y, and the consistent change between those values.
linear model
What is a graph of ordered pairs showing a relationship between two sets of data?
scatterplot
The _____ refers to the consistent change in y for each unit change in x.
slope
Which of the following is NOT an assumption of linear regression?
uniformity
Use a ruler or a graphing calculator to find the regression line of the following data set: (2, 3) (4, 6) (5, 1) (2, 4) (1, 3) (6, 3)
y = -.14x + 3.79
What is the slope intercept formula?
y = mx + b
Find the regression line equation using the formulas for the following data set: (1, 3) (2, 4) (3, 5)
y = x + 2
Imagine you are looking at a graph that shows a correlational line moving from the bottom left corner of the graph to the upper right corner. Which correlation coefficient below would best represent the pattern of data while remaining within the possible range of correct calculations?
+0.72
Which one of the following coefficients indicates that the two variables of interest move in opposite directions while remaining within the possible range of correct calculations?
-0.83
Which one of the following coefficients indicates the strongest relationship between two variables while remaining within the possible range of correct calculations?
-0.83
How many adults picked chocolate or vanilla?
109
How many people surveyed favored football or baseball?
112
Elizabeth wanted to know the gender and the hair color of each of her classmates. She arranged the results of this survey into a two-way table, shown below. According to the table, what is the marginal relative frequency of students in the class that have blonde hair?
29.6%
Elizabeth wanted to know the gender and the hair color of each of her classmates. She arranged the results of this survey into a two-way table, shown below. According to the table, what is the joint relative frequency of boys with red hair?
3/27
Elizabeth wanted to know the gender and the hair color of each of her classmates. She arranged the results of this survey into a two-way table, shown below. According to the table, what is the conditional relative frequency of students that have blonde hair, given that those students are girls?
35%
Elizabeth wanted to know the gender and the hair color of each of her classmates. She arranged the results of this survey into a two-way table, shown below. According to the table, what is the conditional relative frequency of students that are boys, given that those students have brown hair?
41.67%
How many teens would not pick chocolate?
61
How many children and teens eat bananas?
87
How many of the people surveyed favored football or basketball?
90
A scientist plots data points from an experiment, and notices that the dependent variables and the independent variables in the data set are decreasing together. What kind of correlation have they discovered, and why?
A positive correlation, because these describe situations where the dependent variables and the independent variables in a data set increase or decrease together.
What does homoscedasticity imply?
All values of the independent variable have the same variance around the regression line
Find the correlation coefficient that exist between the two variables X and Y as given by the following coordinates. (1,2) (2,1) (2,6) (3,1)
Approximately -0.17
Find the correlation coefficient between the two values. Is there a positive or negative correlation?
Approximately -0.44, Negative Correlation
Find the correlation coefficient between the Average Number of Assignments in Class and the Class Absences. Deduce whether there is a positive or negative correlation
Approximately -0.95, Strong Negative correlation
Find the correlation coefficient, r between the X and Y values. X (4, 4, 6, 5, 4,) / Y (7, 3, 12, 10, 4)
Approximately 0.90
How are independent variables and dependent variables different?
As an experimenter, you can directly change the value of an independent variable, but the value of a dependent variable depends on the outcome of the experiment.
A scientist finishes an experiment, and concludes that there is a causal link between the independent variable and the dependent variable. Why might they come to this conclusion?
Because changes in the independent variable appear to cause changes in the dependent variable.
A scientist is graphing data points from an experiment and concludes that the data set is linear. Which of these statements BEST explains why they drew this conclusion?
Because the relationship between the dependent and independent variables is linear.
A scientist is designing an experiment with rats, and designates weight as the dependent variable. Why might this be the case?
Because the weight will be influenced by an outside factor that the scientist controls.
What do we call two sets of variables that can change and are compared to find relationships?
Bivariate data
How does a regression line show the relationship between two points?
By making a straight line that attempts to fit all of the available data points, it establishes a linear model that should hold approximately for any two points.
What is the relationship between two sets of variables used to describe or predict information?
Correlation
What is the relationship between two variables or sets of data?
Correlation
Which of the following problems could be studied through the use of regression analysis?
How the speeds of runners on a track team relate to how long they each train
What is a condition or piece of data in an experiment that can be controlled or changed?
Independent variable
Dr. Nodd does a study in which she observes parents and their children interacting at home. She finds that the more supportive parents are, the less aggressive their children are. What conclusion can Dr. Nodd make?
Level of support and aggression are negatively correlated.
What is the comparison of two values, usually x and y, and the consistent change between those values?
Linear model
What do we call a prediction where a variable (y) is dependent on a second variable (x) based on the regression equation of a given set of data?
Linear regression
What is it called when dependent variables and independent variables in a data set either increase or decrease opposite from one another?
Negative correlation
What do we call a straight line that attempts to predict the relationship between two points?
Regression line
What is a straight line that attempts to predict the relationship between two points, also known as a trend line or line of best fit?
Regression line
José wants to calculate a correlation; which of the following graphs should he use?
Scatter plot
For the following equation, identify the slope, the intercept, and interpret the meaning of each for the scenario. y = -4x + 7 For every incorrect answer, Stacia loses points. She gets points for writing her name on her paper.
Slope: -4 Intercept: 7 Interpretation: -4 represents the number of points off for each incorrect answer, 7 represents the number of points for writing the name on the paper.
For the following equation, identify the slope, the intercept, and interpret the meaning of each for the scenario. y= 0.03x + 25 Jay just got his water bill. He has to pay an initial fee for the service, plus an amount per gallon that he uses.
Slope: 0.03 Intercept: 25 Interpretation: The 0.03 is the rate per gallon of water, the 25 is the initial fee of the bill
For the following equation, identify the slope, the intercept, and interpret the meaning of each for the scenario. y= 7.5x - 3 James just got a new job. He will make a certain amount of money per hour, but he will also receive a one-time deduction to pay for his new uniform.
Slope: 7.5 Intercept: -3 Interpretation: 7.5 is the amount of money per hour, 3 is how much is deducted for the uniform.
What does normality mean in analyzing residuals?
The residuals are normally distributed around the line of best fit.
In the equation y = 4x +15, what does 15 represent?
The y-intercept
What does statistical independence mean in analyzing residuals?
There is no correlation between residuals within the data set.
The correlation coefficient between the number of girls passing in Physics at grade 9 and the number of girls passing in Physics at grade 11 is 0. Identify the correct statement for the above.
There is no correlation between the number of girls passing in Physics at grade 9 and the number of girls passing in Physics at grade 11
What is a table listing two categorical variables whose values have been paired?
Two-way table