Skip to main content
Ch. 9 - Correlation and Regression
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 9 - Correlation and RegressionProblema 9.2.4
Capitolo 9, Problema 9.2.4

4. For a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

Guida verificata passo dopo passo
1
Understand that the regression line is a model that predicts values of y based on values of x within the range of observed data.
Identify the range of x-values in the original dataset used to create the regression line; these are the minimum and maximum x-values observed.
Recognize that meaningful predictions for y are typically made only for x-values within this observed range, as predictions outside this range involve extrapolation and may be unreliable.
Note that predictions for x-values far outside the observed range can lead to inaccurate or misleading results because the relationship modeled by the regression may not hold beyond the data.
Therefore, the meaningful x-values for prediction are those within the interval from the minimum to the maximum observed x-values in the dataset.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Regression Line and Prediction

A regression line models the relationship between an independent variable x and a dependent variable y, allowing predictions of y based on x values. It summarizes the trend in the data and is used to estimate y for given x inputs.
Video consigliato:
Percorso guidato
04:57
Using Regression Lines to Predict Values

Range of Observed Data (Domain of x)

Meaningful predictions are typically limited to x values within the range of the observed data used to create the regression line. Predictions outside this range, called extrapolation, can be unreliable because the relationship may not hold beyond the observed domain.
Video consigliato:
Percorso guidato
04:39
Visualizing Qualitative vs. Quantitative Data

Extrapolation vs. Interpolation

Interpolation refers to predicting y for x values within the observed data range, which is generally reliable. Extrapolation involves predicting y for x values outside this range and is less reliable because the model’s assumptions may not apply beyond the data.
Video consigliato:
Percorso guidato
04:39
Visualizing Qualitative vs. Quantitative Data
Pratica correlata
Domanda del libro di testo

"Predicting y-Values In Exercises 3-6, use the multiple regression equation to predict the y-values for the values of the independent variables.

3. Cauliflower Yield The equation used to predict the annual cauliflower yield (in pounds

per acre) is y=24,791+4.508x_1-4.723x_2

where x_1 is the number of acres planted and x_2 is the number of acres harvested.(Adapted from United States Department of Agriculture)

a. x_1 = 36,500, x_2 = 36,100

b. x_1 = 38,100, x_2 = 37,800

c. x_1 = 39,000, x_2 = 38,800

d. x_1 = 42,200, x_2 = 42,100"

33
views
Domanda del libro di testo

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

65
views
Domanda del libro di testo

"[APPLET] Registered Nurse Salaries In Exercises 27–30, use the table, which shows the years of experience of 14 registered nurses and their annual salaries (in thousands of dollars). (Adapted from Payscale, Inc.)

27. Correlation Using the scatter plot of the registered nurse salary data shown below, what type of correlation, if any, do you think the data have? Explain.


"

82
views
Domanda del libro di testo

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight

loss."

79
views
Domanda del libro di testo

2. Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

118
views
Domanda del libro di testo

1. Interpret the meaning of the coefficient -8.2 in the multiple regression equation y=112.1+0.43x_1-8.2x_2+29.5x_3.

70
views