Question

There is a linear relationship between the number of cricket chirps and the temperature of the air. A biologist developed the regression model $y=$ $24.9+3.5 x$ , valid for values of $x$ between 10 and $24 .$ In this model $x$ is the number of chirps per minute and $y$ is the predicted temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 8 chirps per minute? (A) $3.5^{\circ}$ (B) $24.9^{\circ}$ (C) $28^{\circ}$ (D) $28.4^{\circ}$ (E) $52.9^{\circ}$

Name: Problem 8, Chapter :
Uploaded: 2019-08-31T01:11:37-08:00
Duration: 2 min 5 s
Channel: Dilip Paruchuri

   There is a linear relationship between the number of cricket chirps and the
temperature of the air. A biologist developed the regression model $y=$
$24.9+3.5 x$ , valid for values of $x$ between 10 and $24 .$ In this model $x$ is the number of chirps per minute and $y$ is the predicted temperature in
degrees Fahrenheit. What is the estimated increase in temperature that
corresponds to an increase of 8 chirps per minute?
(A) $3.5^{\circ}$
(B) $24.9^{\circ}$
(C) $28^{\circ}$
(D) $28.4^{\circ}$
(E) $52.9^{\circ}$

Instant Answer

Solved by Expert Dilip Paruchuri

08/31/2019

Step 1

9+3.5x$ where $x$ is the number of chirps per minute and $y$ is the predicted temperature in degrees Fahrenheit. We are asked to find the estimated increase in temperature that corresponds to an increase of 8 chirps per minute. This is essentially asking us to find Show more…

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There is a linear relationship between the number of cricket chirps and the temperature of the air. A biologist developed the regression model $y=$ $24.9+3.5 x$ , valid for values of $x$ between 10 and $24 .$ In this model $x$ is the number of chirps per minute and $y$ is the predicted temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 8 chirps per minute? (A) $3.5^{\circ}$ (B) $24.9^{\circ}$ (C) $28^{\circ}$ (D) $28.4^{\circ}$ (E) $52.9^{\circ}$

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Key Concepts

Linear Regression

Linear regression is a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.

Slope Interpretation

In the context of linear regression, the slope represents the change in the predicted outcome for a one-unit increase in the predictor variable. This interpretation allows for understanding how variations in the predictor are expected to influence the response variable.

Unit Rate Analysis

Unit rate analysis involves using the slope number directly to compute the predicted change in the outcome variable corresponding to any given change in the predictor variable by multiplying the slope by the number of units changed.

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