Linear Regression Application, Interpolation and Extrapolation Use the data and story to answer the following questions The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 1 11.5 y 13.9 10.9 9.9 | 6.6 6.1 | 6.2 | 6.3 4.8 8.3 6.6 3.4 2.5 2.7 2.6 0.5 z = thousands of automatic weapons y = murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places) Determine the regression equation in y = ax + b form and write it below. A) How many murders per 100,000 residents can be expected in a state with 2.6 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 9.7 thousand automatic weapons? Round to 3 decimal places. Answer =
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![Linear Regression Application, Interpolation and Extrapolation
Use the data and story to answer the following questions
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
x & 11.5 & 8.3 & 6.6 & 3.4 & 2.5 & 2.7 & 2.6 & 0.5 \\
\hline
y & 13.9 & 10.9 & 9.9 & 6.6 & 6.1 & 6.1 & 6.3 & 4.8 \\
\hline
\end{array}
\]
\( x = \) thousands of automatic weapons
\( y = \) murders per 100,000 residents
Use your calculator to determine the equation of the regression line. (Round to 2 decimal places)
Determine the regression equation in \( y = ax + b \) form and write it below.
\[
\text{Equation:}
\]
A) How many murders per 100,000 residents can be expected in a state with 2.6 thousand automatic weapons?
Answer = ________ Round to 3 decimal places.
B) How many murders per 100,000 residents can be expected in a state with 9.7 thousand automatic weapons?
Answer = ________ Round to 3 decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9849c3b-f0ff-47eb-829a-2c91d3fc6b02%2F889a6d4a-62f2-4655-9e18-cfedabd93d17%2F9odybwa_processed.png&w=3840&q=75)
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