Exam 16: Regression Models for Nonlinear Relationships

The following data, with the corresponding Excel scatterplot, show the average growth rate of Weeping Higan cherry trees planted in Washington, DC. At the time of planting, the trees were one year old and were all six feet in height. Which of the following is the correlation coefficient between Height and ln(Age)?

The following data, with the corresponding scatterplot, show the average growth rate of Weeping Higan cherry trees planted in Washington, DC. At the time of planting, the trees were one year old and were all six feet in height. If the age of a tree increases by 1%, then its predicted height increases by approximately ________.

The logarithmic model is especially attractive when only the ________ variable is better captured in percentages.

For the exponential model ln(y) = β₀ + β₁x + ε, β₁ × 100% is the approximate percentage change in E(y) when x increases by 1%.

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region. The linear model Pepsi Sales = β₀ + β₁Pepsi Price + β₂Cola Price + ε and the log-log model ln(Pepsi Sales) = β₀ + β₁ln(Pepsi Price) + β₂ln(Cola Price) + ε have been estimated as follows: What is the percentage of variations in the log of the Pepsi sales explained by the log-log model?

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region. The linear model Pepsi Sales = β₀ + β₁Pepsi Price + β₂Cola Price + ε and the log-log model ln(Pepsi Sales) = β₀ + β₁ln(Pepsi Price) + β₂ln(Cola Price) + ε have been estimated as follows: Using the log-log model, calculate the predicted Pepsi Sales when the Pepsi Price is $1.50 and the Cola Price is $1.25.

A model in which both the response variable and the explanatory variable have been log transformed is called a(n) ________.

Thirty employed single individuals were randomly selected to examine the relationship between their age (Age) and their credit card debt (Debt) expressed as a percentage of their annual income. Three polynomial models were applied and the following table summarizes Excel's regression results. What is the regression equation that provides the best fit?

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region. The linear model Pepsi Sales = β₀ + β₁Pepsi Price + β₂Cola Price + ε and the log-log model ln(Pepsi Sales) = β₀ + β₁ ln(Pepsi Price) + β₂ ln(Cola Price) + ε have been estimated as follows: Using the linear model and holding Cola Price constant, what is the predicted change in the Pepsi Sales if the Pepsi Price increases by 10 cents?

How many coefficients need to be estimated in the quadratic regression model?

For the logarithmic model ln(y) = β₀ + β₁ln(x) + ε, the predicted value of y is computed as ________.

The following data show the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180º F. The output for an exponential model, ln(Temp) = β₀ + β₁Time + ε, is below. What is the predicted coffee temperature in half an hour after the brewing?

The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model. Which of the following is the predicted productivity when 32 workers are hired?

The following data, with the corresponding Excel scatterplot, show the average growth rate of Weeping Higan cherry trees planted in Washington, DC. At the time of planting, the trees were one year old and were all six feet in height. If a cherry tree is planted as a one-year-old and six-foot-tall tree, which of the following is the estimated time needed by the tree to reach 16.5 feet in height?

Which of the following regression models is most likely to provide the best fit for the data represented by the following scatterplot?

The log-log regression model is ________ in the variables.

The following data, with the corresponding Excel scatterplot, show the average growth rate of Weeping Higan cherry trees planted in Washington, DC. At the time of planting, the trees were one year old and were all six feet in height. What is the regression model used to describe the relationship between Height and Age?

Which of the following regression models is most likely to provide the best fit for the data represented by the following scatterplot?

The log-log and the ________ models can have similar shapes.

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region. The linear model Pepsi Sales = β₀ + β₁Pepsi Price + β₂Cola Price + ε and the log-log model ln(Pepsi Sales) = β₀ + β₁ln(Pepsi Price) + β₂ln(Cola Price) + ε have been estimated as follows: What is the percentage of variations in the Pepsi sales explained by the linear model?