Math Problem Statement

Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is​ linear, determine whether it indicates a positive or negative association between the variables.

Use this information to answer the following.

020400102030ExplanatoryResponse

A scatter diagram has a horizontal axis labeled “Explanatory” from 0 to 40 plus in increments of 10 and a vertical axis labeled “Response” from 0 to 30 in increments of 5. The following 18 approximate points are plotted, listed here from left to right: (5, 29); (5, 26); (10, 25); (12, 24); (15, 24); (15, 21); (18, 22); (21, 21); (21, 18); (25, 19); (25, 16); (30, 16); (30, 13); (35, 14); (42, 10); (42, 8); (50, 6); (50, 4). The points generally fall from left to right at a constant rate.

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Part 1

Do the two variables have a linear​ relationship?

A.

The data points do not have a linear relationship because they lie mainly in a straight line.

B.

The data points have a linear relationship because they do not lie mainly in a straight line.

C.

The data points have a linear relationship because they lie mainly in a straight line.

D.

The data points do not have a linear relationship because they do not lie mainly in a straight line.

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Relationship
Scatter Plot
Negative Association

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

Linear Regression Theorem
Correlation Coefficient

Suitable Grade Level

Grades 9-11