Regression Equations and Residuals

Estimate the correlation coefficient.

• r = -0.8

• r = -0.5

• r = 0.5

• r = 0.8

In the years from 1900-2020, the US Population for people aged 65 and over has been increasing. An exponential regression was used to develop a model for the population. The figure above shows a graph of the residuals of the exponential regression. Which of the following statements about the exponential regression is true?

• The residual plot has no apparent pattern, so the exponential model was not appropriate.

• The residual plot has no apparent pattern, so the exponential model was appropriate.

• The residual plot displays a pattern, so the exponential model was not appropriate.

• The residual plot displays a pattern, so the exponential model was appropriate.

The table shows the population P, in thousands of endangered birds introduced into a new protected bird sanctuary, for the years 2020 - 2023. A linear regression y = a + bx is used to model the function P. What is the residual for the number of birds, in thousands, in the year 2023 (t = 3)?

• 0.0142

• -0.0146

• 0.0148

• 5.3156

• 19.503

• 20.201

• 20.422

• 31.859

A set of data is shown on the semi-log plot. If an exponential regression is used to model the data, which of the following claim and explanation statements best fit this data?

• The residual plot will show a clear patter, because the exponential model was not appropriate.

• The residual plot will show no clear pattern, because the exponential model was not appropriate.

• The residual plot will show no clear pattern, because the exponential model was appropriate.

• The residual plot will show a clear pattern, because the exponential model was appropriate.

• This residual plot represents a linear fit.
• This residual plot represents a nonlinear fit.
• This residual plot represents no fit.

If the point with the red x is removed from the scatterplot, what will happen to the slope of the LSRL and the correlation coefficient?

• slope increases, r increases

• slope decreases, r increases

• slope increases, r decreases

• slope decreases, r decreases

• slope is unchanged, r increases

The residual plots from five different least squares regression lines are shown below. Which of the plots shows the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?

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What is the value of the correlation coefficient?

• 0.891

• -0.891

• 0.875

• 0.943

• -0.943

Y-hat is the ________ value of y for a given value of x.