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A high school administrator is interested in determining the relationship between high school students' final grades in geometry and chemistry. She randomly samples 400 students who took both classes and records their final scores (out of 100 points) and carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable, since the students take chemistry before geometry. The resulting data was used to produce the following output.
Simple linear regression results:
Dependent Variable: Geometry
Independent Variable: Chemistry
Geometry = 3.6276926 + 0.91857341*Chemistry
Sample size: 400
R2= 0.55808158
Estimate of error standard deviation: 9.417521
Which of the following is a reasonable interpretation of the slope of this simple linear regression?
a. The slope of this regression cannot be interpreted because 0 is not in the range of chemistry scores.
b. Getting high grades in chemistry lead students to achieve high grades in geometry.
c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score.
d. On average, a 1 percentage point difference in geometry score is associated with a 0.919 percentage point difference in chemistry score.

Sagot :

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Answer: c. On average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score

Step-by-step explanation:

Given that:

Slope value = 0.91857341

The dependent and independent variables are ;

Dependent Variable: Geometry

Independent Variable: Chemistry

Slope is the rate of change in the dependent variable per unit change in the independent variable.

Hence, from the information given, we can conclude that for every 1% change in chemistry score (independent variable), there is a corresponding approximately 0.919% change in geometry score (dependent variable).

From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.

Given :

  • She randomly samples 400 students who took both classes and records their final scores (out of 100 points).
  • She carries out a simple linear regression, using the geometry grade as the response variable and the chemistry grade as the explanatory variable since the students take chemistry before geometry.

Given the simple linear regression results that are:

The Dependent variable is Geometry.

The Independent variable is Chemistry.

Geometry = 3.6276926+0.91857341[tex]\times[/tex]Chemistry

Comparing the above equation with the slope-intercept form which is given by:

y = mx + c

Therefore, slope, m = 0.91857341.

It is also given that:

Sample size is 400

R2= 0.55808158

Estimate of error standard deviation: 9.417521

From the given data it can be concluded that on average, a 1 percentage point difference in chemistry score is associated with a 0.919 percentage point difference in geometry score. Hence option c) is correct.

For more information, refer to the link given below:

https://brainly.com/question/12402189

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