In the equation _{Savings=\beta_0+\beta_1Income+\mu}. What is the residual for the 10th observation if \hat{savings}=$400 and savings=$1000?

Question

BlackTom AI · Accepted Answer

Question restatement: The equation for savings is Savings = β0 + β1 Income + μ, and we’re asked to find the residual for the 10th observation given that the predicted savings hat{Savings} = 400 and the actual savings is 1000.

First, recall the definition of a residual in regression: residual = observed value − predicted value.

Applying this to the 10th observation:
- Observed savings = 1000
- Predicted savings hat{Savings} = 400

Compute the residual: 1000 − 400 = 600.

Now consider the answer option provided: "$600". This matches the calculated residual value exactly.

Why the other potential interpretations would be incorrect (if you consider alternatives):
- If one mistakenly used predicted minus observed, the residual would be 400 − 1000 = −600, which is not the standard residual definition.
- If one confused residual with the forecast error or misread the variables, they might arrive at a different magnitude or sign, but the conventional residual formula is observed minus predicted, yielding +600 in this case.

Summary: The residual for the 10th observation is 600, aligning with the standard residual calculation and the given option "$600".

In the equation _{Savings=\beta_0+\beta_1Income+\mu}. What is the residual for the 10th observation if \hat{savings}=$400 and savings=$1000?Single choice

Similar Questions

Question at position 4 The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.constant termresidualerror termmodel parameterClear my selection

A regression model made a prediction that a particular participant should have a value of 17. However, the actual data point instead has a value of 10. What term refers to the difference between the predicted value and the actual value?

What is the name of the distance captured by the purple dotted line (shown below)?

If our model says this: Salary = B1 + B2*Hits + e And B1 = 10 and B2 = 3. What is the e for a player who has 9 hits and a salary of 57?

Refer to Scenario 8-13. d) The actual girls’ FSL high jump champion in 2014 was Naomi Jimenez from Westtown School, who jumped 62 inches that day. Calculate her residual.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler