Question

1. What do we mean by the direction of the linear relationship between two variables?

Group of answer choices

Direction is used to describe possible directions when arrows are placed on the points

Direction is used to describe if the points are pointing North or South

Direction is used to describe if the points are pointing east or west

Direction describes if the points are rising or falling as you go from left to right

2. Describe the strength and direction of the linear relationship between two variables in which the value of r is between 0.7 and 1

Group of answer choices

strong and moderate

strong and positive

strong and negative

weak and positive

3. True or False: when two variables are strongly correlated, the independent variable causes the dependent variable to behave as observed

Group of answer choices

true

false

4. The regression line can be used to predict the value of the independent variable (x).

Group of answer choices

False

True

Answer 1

1) True option :- Direction describes if the points are rising or falling as you go from left to right

The Direction of a Relationship :-

The correlation measure tells us about the direction of the relationship between the two variables. The direction can be positive or negative.

1. Positive: In a positive relationship both variables tend to move in the same direction: If one variable increases, the other tends to also increase. If one decreases, the other tends to also.

   In the example above, GPA and MathSAT are positively related. As GPA (or MathSAT) increases, the other variable also tends to increase.

2. Negative: In a negative relationship the variables tend to move in the opposite directions: If one variable increases, the other tends to decrease, and vice-versa.

The direction of the relationship between two variables is identified by the sign of the correlation coefficient for the variables. Postive relationships have a "plus" sign, whereas negative relationships have a "minus" sign.

2) True option:- strong and positive

Generally, a value of r greater than 0.7 is considered a strong correlation. Anything between 0.5 and 0.7 is a moderate correlation, and anything less than 0.4 is considered a weak or no correlation.

Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship via a firm linear rule.

3) True because an independent variable is the variable that is changed or controlled in a scientific experiment to test the effects on thedependent variable. A dependent variable is the variable being tested and measured in a scientific experiment. The dependent variable is 'dependent' on the independent variable.

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables.

4) False because the goal in regression analysis is to create a mathematical model that can be used to predict the values of a dependent variable based upon the values of an independent variable. In other words, we use the model to predict the value of Y when we know the value of X. (The dependent variable is the one to be predicted).