Explanation Given info: In the data of 9 custom homes currently listed for sale, the random variable x denotes size in hundreds of square feet and the random variable y denotes price in thousands of dollars. The given level of significance is α = 0.01 . Justification: Standard error of estimate: The residual is defined as e = y ^ − y where y ^ be the predicted value of the response variable and y be the actual value of the response variable. For a set of n observations the standard error of estimate is given as, s e = S S E n − 2 where SSE is the error sum of squares . Standard error of estimate: Software procedure: Step by step procedure to obtain standard error of estimate using Minitab software is given as, Choose Stat > Regression > Fitted Line Plot . In Response ( Y ) , enter the numeric column containing the response data. In Predictor ( X ) , enter the numeric column containing the predictor variable. Click OK . The output using Minitab software is given as, Thus, the standard error of estimate is s e = 59.6208 . The hypotheses are stated as given below: Null hypothesis: H 0 : β 1 = 0 That is, x is not useful for predicting y Alternative hypothesis: H 0 : β 1 ≠ 0 That is, x is useful for predicting y Degrees of freedom: For sample size n the degrees of freedom is n − 2 . Here, the sample size 9 d .f . = n − 2 = 9 − 2 = 7 Thus, the degrees of freedom is 7. Critical value: The level of significance is α = 0.01 α 2 = 0.01 2 = 0.005 From the table IV in Appendix A, critical values for t -test with degrees of freedom as 7 at α 2 = 0.005 is 3.499. Since, t -distribution is symmetric the critical value is ± 3.499 Standard error of estimate: The standard error of estimate is s e given by the formula, S x x = ∑ i x i 2 − ( ∑ i x i ) 2 n . Now, x i y i x i 2 26 540 676 27 555 729 33 575 1,089 29 577 841 29 606 841 34 661 1,156 30 738 900 40 804 1,600 22 496 484 270 5,552 8,316 Thus, for sample size n = 9 , ∑ i x i = 270 , ∑ i x i 2 = 8 , 316

10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 15.2, Problem 60E

To determine

Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15.2, Problem 59E

Chapter 15.2, Problem 61E

Students have asked these similar questions

Pls help asap

Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.

ged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).

Chapter 15 Solutions

Introductory Statistics (10th Edition)

Ch. 15.1 - Suppose that x and y are predictor and response...Ch. 15.1 - Prob. 2E Ch. 15.1 - Prob. 3E Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - In Exercises 15.315.6, assume that the variables...Ch. 15.1 - The difference between an observed value and a...Ch. 15.1 - Identify two graphs used in a residual analysis to...Ch. 15.1 - Which graph used in a residual analysis provides...Ch. 15.1 - Figure 15.8 shows three residual plots and a...

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

Solution Summary: The author evaluates whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

Videos

Decide at the specific significance level whether the data provide sufficient evidence to conclude that predictor variable is useful for predicting the response variable.

Want to see the full answer?

Chapter 15 Solutions