
Concept explainers
(a) Explain the logic of the ordinary least squares (OLS) method. (b) How are the least squares formulas for the slope and intercept derived? (c) What sums are needed to calculate the least squares estimates?
a.

Explain the logic of the ordinary least squares method.
Explanation of Solution
Ordinary least squares method:
For getting the best fit of regression, ordinary least square method can be used. The slope and the intercept are estimated in the way that the residual sum of squares will be minimized.
If only the sum of residuals has used for minimizing the error, there is possibility that the positive and the negative error will be dismissed. Therefor it is logical to use the sum of squares for minimizing the residual.
b.

Show how the least squares formula for the slope and the intercept was derived.
Explanation of Solution
Calculation:
Let Y is the response variable and X is the predictor variable. The linear regression line is
The error sum of squares is,
For minimizing the sum of squares, the expression should be derivative by
Now, equating the derivatives with 0,
Hence, the least square estimator of
c.

Explain the sums which should be calculated for finding the least squares estimators.
Explanation of Solution
For finding the least square estimates,
Want to see more full solutions like this?
Chapter 12 Solutions
Gen Combo Ll Applied Statistics In Business & Economics; Connect Access Card
- Harvard University California Institute of Technology Massachusetts Institute of Technology Stanford University Princeton University University of Cambridge University of Oxford University of California, Berkeley Imperial College London Yale University University of California, Los Angeles University of Chicago Johns Hopkins University Cornell University ETH Zurich University of Michigan University of Toronto Columbia University University of Pennsylvania Carnegie Mellon University University of Hong Kong University College London University of Washington Duke University Northwestern University University of Tokyo Georgia Institute of Technology Pohang University of Science and Technology University of California, Santa Barbara University of British Columbia University of North Carolina at Chapel Hill University of California, San Diego University of Illinois at Urbana-Champaign National University of Singapore McGill…arrow_forwardName Harvard University California Institute of Technology Massachusetts Institute of Technology Stanford University Princeton University University of Cambridge University of Oxford University of California, Berkeley Imperial College London Yale University University of California, Los Angeles University of Chicago Johns Hopkins University Cornell University ETH Zurich University of Michigan University of Toronto Columbia University University of Pennsylvania Carnegie Mellon University University of Hong Kong University College London University of Washington Duke University Northwestern University University of Tokyo Georgia Institute of Technology Pohang University of Science and Technology University of California, Santa Barbara University of British Columbia University of North Carolina at Chapel Hill University of California, San Diego University of Illinois at Urbana-Champaign National University of Singapore…arrow_forwardA company found that the daily sales revenue of its flagship product follows a normal distribution with a mean of $4500 and a standard deviation of $450. The company defines a "high-sales day" that is, any day with sales exceeding $4800. please provide a step by step on how to get the answers in excel Q: What percentage of days can the company expect to have "high-sales days" or sales greater than $4800? Q: What is the sales revenue threshold for the bottom 10% of days? (please note that 10% refers to the probability/area under bell curve towards the lower tail of bell curve) Provide answers in the yellow cellsarrow_forward
- Find the critical value for a left-tailed test using the F distribution with a 0.025, degrees of freedom in the numerator=12, and degrees of freedom in the denominator = 50. A portion of the table of critical values of the F-distribution is provided. Click the icon to view the partial table of critical values of the F-distribution. What is the critical value? (Round to two decimal places as needed.)arrow_forwardA retail store manager claims that the average daily sales of the store are $1,500. You aim to test whether the actual average daily sales differ significantly from this claimed value. You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. Showing the calculation is a must. If calculation is missing,so please provide a step by step on the answers Numerical answers in the yellow cellsarrow_forwardShow all workarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning

