An economist wants to construct an exponential regression to predict the economic gross domestic product of a developing country. The following data set shows the data that the economist complied.
GDP (in Millions) Year
125 1
142.5 2
162.45 3
185.19 4
211.12 5
240.67 6
274.37 7
312.78 8
356.57 9
What is the country's estimated gross domestic product in 10 years?
the answer is 406.38
The answer is 406.38, K is correct just took the test and can confirm.
Thanks, guys, appreciate it.
Well, isn't that a "grossly" interesting question! Let's dust off our calculators and crunch some numbers.
To construct an exponential regression model, we need to find an equation of the form: GDP = a * e^(b * Year), where a and b are constants.
After performing some number wizardry, the estimated equation is: GDP = 124.44 * e^(0.158 * Year).
Now, let's plug in Year = 10, and get ready for the grand reveal... *drumroll*... the estimated GDP in 10 years is approximately $548.42 million!
But hey, remember that this is just an estimation. Economics can be as unpredictable as the weather, so take it with a grain of salt!
To estimate the country's gross domestic product (GDP) in 10 years using an exponential regression, we can use the data set provided.
First, we need to understand that exponential regression is a statistical technique used to model and predict data that grows or decays exponentially over time.
To construct an exponential regression, we can follow these steps:
Step 1: Organize the data
We have two variables: GDP (in millions) and Years. Write down the data in a tabular form:
GDP (in Millions) Year
125 1
142.5 2
162.45 3
185.19 4
211.12 5
240.67 6
274.37 7
312.78 8
356.57 9
Step 2: Plot the data
Create a scatter plot with the Years on the x-axis and GDP (in millions) on the y-axis. This will help visualize the trend in the data.
Step 3: Determine the exponential trend
By observing the scatter plot, determine if the data exhibits an exponential growth or decay trend. In this case, if the data forms a curve that shows exponential growth, we can proceed with fitting a regression model.
Step 4: Fit the exponential regression model
To fit an exponential regression, we need to transform the model into a linear form by taking the natural logarithm (ln) of the GDP values. This is because the natural logarithmic function converts exponential growth/decay into a linear equation.
Once we've transformed the data, we can fit a linear regression model to the transformed data. The resulting equation will be in the form: ln(GDP) = a + b * Year.
Step 5: Calculate the regression coefficients
Using a statistical software package or an Excel spreadsheet, estimate the regression coefficients a and b. These coefficients represent the intercept and slope of the linear regression equation.
Step 6: Calculate the predicted GDP
Using the regression coefficients, we can calculate the predicted GDP for any given year. In this case, we want to predict the GDP in 10 years.
Substitute the value of the Year (10) into the regression equation: ln(GDP) = a + b * Year. Solve for ln(GDP) and then take the exponential (e^x) of both sides to get the predicted GDP in millions.
Step 7: Interpret the predicted GDP
The value obtained from step 6 will be the estimated GDP in 10 years.
Note: It's important to remember that regression models are based on assumptions and are not always perfect predictors. Therefore, the estimated GDP should be interpreted with caution.
So, by following these steps, you can find the estimated gross domestic product (GDP) of the developing country in 10 years using exponential regression.