In 9-13 : a. Create a scatter plot for the data. b....

In $9-13 :$ a. Create a scatter plot for the data. b. Determine which regression model is the most appropriate for the data. Justify your answer. c. Find the regression equation. Round the coefficient of the regression equation to three decimal places. $$ \begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {3.3} & {-3.8} & {-2.1} & {0.4} & {3.5} & {-3.8} & {-1.8} & {-0.4} & {2.4} & {1.2} \\ \hline y & {12.5} & {-17.1} & {-3.6} & {0.4} & {15.0} & {-18.9} & {-2.1} & {-0.4} & {4.2} & {3.4} \\ \hline\end{array} $$

In $9-13 :$ a. Create a scatter plot for the data. b. Determine which regression model is the most appropriate for the data. Justify your answer. c. Find the regression equation. Round the coefficient of the regression equation to three decimal places.
$$
\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {3.3} & {-3.8} & {-2.1} & {0.4} & {3.5} & {-3.8} & {-1.8} & {-0.4} & {2.4} & {1.2} \\ \hline y & {12.5} & {-17.1} & {-3.6} & {0.4} & {15.0} & {-18.9} & {-2.1} & {-0.4} & {4.2} & {3.4} \\ \hline\end{array}
$$

Key Concepts

Regression Model Selection

Regression model selection involves choosing the most appropriate mathematical model to describe the relationship between an independent and a dependent variable based on data visualization and statistical criteria. After examining the scatter plot, one evaluates if a linear model or another type of regression (e.g., quadratic, exponential) best captures the underlying pattern. Justification depends on the observed alignment of data points along a common trend line or curve.

Regression Equation

A regression equation represents the mathematical relationship between the independent and dependent variables, often in the form of y = mx + b for a linear model, where m is the slope and b is the y-intercept. It is derived using statistical methods that minimize the discrepancies between the observed values and the values predicted by the model. Coefficients in the equation are typically rounded to a specified number of decimal places to simplify interpretation, while still maintaining an acceptable level of precision.

Scatter Plot

A scatter plot is a graphical representation of paired numerical data. It is used to visually assess the relationship between two variables by plotting one variable along the horizontal axis and the other along the vertical axis. This method can help identify patterns, trends, or outliers and is often the first step in determining the appropriate statistical model to describe the data.

Transcript

00:01 All right, so we're given a data set, and we want us to create a scatter plot first.

00:06 So i'm using desmos.

00:07 It's an online graphing calculator.

00:09 And so i'm going to go over here to this plus, and i'm going to add a table, and i'm going to actually enter that table that's in the problem.

00:18 So my x values are 3 .3, negative 3 .8, negative 2 .1, 0 .4, 3 .5, negative 3 .8.

00:36 Negative 1 .8.

00:38 I'm just entering this table.

00:40 So once the x's are in, i'm going to go back and put the y values that correspond.

01:23 Now once the data's in, if your graph doesn't change to fit your data, you can always go in and change that window.

01:30 Use the wrench up in the top right.

01:34 And we can change this so that it fits.

01:39 Notice that your x values, lowest one looks like it's at negative 4.

01:44 So we could change this maybe to negative 5.

01:48 The highest one looks to be around, so maybe negative 5 to 5.

01:53 As far as your y values, your lowest number looks like it's at negative 18.

01:58 So maybe we do negative 20.

02:02 All the way up to i see a positive 15.

02:06 So let's just do negative 20 to positive 20.

02:09 Clicking out, you can see that this curve, these points here, it's starting in the bottom left, going up through 0.

02:16 To the top right.

02:18 That's a cubic function if i've ever seen one...

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