Question

which of the following best describes the purpose of a regression line in statistics?
to predict the value of one variable based on the value of another variable
to calculate the probability of an event.
to find the mean of a data set.
to determine the mode of a data set.
question 6
given the regression equation y=2x+5, what is the value of y when x=3?
5 pts

Explanation:

First Question (Purpose of Regression Line)

• A regression line in statistics is used to model the relationship between two variables (independent and dependent) to predict the value of the dependent variable using the independent variable.
• Calculating probability is related to probability theory, not regression.
• Finding the mean involves summing values and dividing by count, not regression.
• Determining the mode is about the most frequent value, not regression.

So the correct option is the one about predicting one variable from another.

Step1: Identify the equation and input

We have the regression equation $y = 2x + 5$ and we need to find $y$ when $x = 3$.

Step2: Substitute $x = 3$ into the equation

Substitute $x = 3$ into $y = 2x + 5$. So we calculate $y = 2(3) + 5$.

Step3: Perform the arithmetic operations

First, calculate $2(3)=6$. Then, add 5 to 6: $6 + 5 = 11$.

Answer:

To predict the value of one variable based on the value of another variable

Second Question (Regression Equation Calculation)