Regression Analysis Quiz

Using technology, find the least-squares regression line relating the revenue from natural resources and the GDP. Be sure to define any variables used.

• The regression line is y = 0.5x + 2

• The regression line is y = 1.2x - 3

• The regression line is y = -0.8x + 5

• The regression line is y = 2x + 1

Use the least-squares regression line to predict the GDP for a country with a revenue of $50 billion from natural resources.

• $1 trillion

• $500 billion

• $750 billion

• $1.5 trillion

The amount of sugar, in grams, and the number of calories in a 12-ounce serving of 10 different popular soft drinks are shown in the scatterplot. The scatterplot with the least-squares regression line and the residual plot are shown. The sum of the squared residuals is 2219.9. Which point contributes the most to this sum?

• Point A

• Point B

• Point C

• Point D

Is a linear model appropriate for these data? Explain.

• Yes, because the data shows a linear trend.

• No, because the data does not show a linear trend.

• Yes, because linear models are always appropriate.

• No, because linear models are never appropriate.

The scatterplot shows the mean annual precipitation (in centimeters) and the mean annual temperature (in °C) for 21 different forest regions. What is the relationship between mean annual precipitation and mean annual temperature?

• There is a positive correlation.

• There is a negative correlation.

• There is no correlation.

• The correlation cannot be determined from the scatterplot.

The scatterplot shows the mean annual precipitation (in centimeters) and the mean annual temperature (in °C) for 21 different forest regions. Write an equation for the least-squares regression line. Be sure to define any variables used.

• y = 0.5x + 10

• y = 1.2x - 5

• y = -0.8x + 20

• y = 2x + 15

The scatterplot shows the mean annual precipitation (in centimeters) and the mean annual temperature (in °C) for 21 different forest regions. Wet tropical forests are designated as areas with 140 to 220 cm of precipitation per year. What is the predicted mean annual temperature range for these forests?

• 15°C to 25°C

• 20°C to 30°C

• 25°C to 35°C

• 30°C to 40°C

The scatterplot shows the total annual revenue (in billions of dollars) for the social media website Facebook, for each year from 2010 to 2022 recorded as years since 2000. The least-squares regression line for the relationship is ŷ = -121.89 + 10.33x. Calculate and interpret the residual for the year 2016 if the actual revenue was $27.64 billion.

• 1.23 billion

• 2.45 billion

• 3.67 billion

• 4.89 billion

Without any calculations, use the scatterplot and the graph of the least squares regression line to estimate the residual for the year 2021.

• Approximately 0.5

• Approximately 1.0

• Approximately -0.5

• Approximately -1.0

Sketch a residual plot for the data on the axes given by approximating each residual.

• Option A: Plot the residuals against the predicted values.

• Option B: Plot the residuals against the actual values.

• Option C: Plot the residuals against the time order of data collection.

• Option D: Plot the residuals against the independent variable.