# Simple Linear Regression Results## Overview- **Dependent Variable:** DIAMETER- **Independent Variable:** RATO### Regression Equation:\[ DIAMETER = -1314.0475 + 199.06132 \times RATO \]### Sample Size:- 13### Statistical Measures:- **Correlation Coefficient (R):** 0.97602564- **R-squared (R-sq):** 0.95262604- **Estimate of Error Standard Deviation:** 45.080042## Parameter Estimates| Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value ||------------|------------|-----------|-------------|----|------------|---------|| Intercept | -1314.0475 | 110.80982 | ≠ 0 | 11 | -11.858583 | <0.0001 || Slope | 199.06132 | 13.384407 | ≠ 0 | 11 | 14.872629 | <0.0001 |## Analysis of Variance Table for Regression Model| Source | DF | SS | MS | F-stat | P-value ||--------|----|------------|----------|----------|---------|| Model | 1 | 449514.92 | 449514.92| 221.19509| <0.0001 || Error | 11 | 22354.312 | 2032.2102| | || Total | 12 | 471869.23 | | | | ### Explanation:- **DF (Degrees of Freedom):** Represents the number of independent values or quantities that can vary in an analysis without breaking any constraints.- **SS (Sum of Squares):** Measures the total variation.- **MS (Mean Square):** Average of the squared differences (SS/DF).- **F-statistic:** A ratio of two variances and is used to test the hypothesis that the model fits well.- **P-value:** Indicates the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is correct. **Exercise 11.37: Repair and Replacement Costs of Water Pipes**This exercise refers to a study of water pipes as discussed in the IHS Journal of Hydraulic Engineering, particularly in the September 2012 issue. The study is detailed in Exercise 11.21 on page 630 of the journal. For this exercise, you will need to refer to a Minitab simple linear regression printout found on page 631. This printout relates the variable $ y $ (the ratio of repair to replacement cost of commercial pipes) to the variable $ x $ (the diameter of the pipe in millimeters).**Tasks:**a. **Locate the value of $ s $ on the printout.**b. **Provide a practical interpretation of $ s $.**This exercise involves applying statistical methods to real-world engineering problems, giving students the opportunity to connect theoretical concepts with industry applications.

a. The notation s represents the value of the standard error of the model and in the given model the…

Answered: 11.37 Repair and replacement costs of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is: kids; = Bo + B1educ; + uż. 1. What are the parameters in the model? 2. What kinds of factors are contained in u? Are these likely to be cor- related with level of education? 3. Will a simple regression analysis uncover the ceteris paribus effect of education on fertility? Explain.
Last ride Consider the roller coasters described inExercise 26 again. The regression analysis gives themodel Duration = 64.232 + 0.180 Drop.a) Explain what the slope of the line says about howlong a roller coaster ride may last and the height of thecoaster.b) A new roller coaster advertises an initial drop of200 feet. How long would you predict the rides last?c) Another coaster with a 150-foot initial drop advertisesa 2-minute ride. Is this longer or shorter than you’dexpect? By how much? What’s that called?
Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose that someone wants to predict the cost of dinner at a restaurant in a city based on the Zagat food quality ratings. If 10 restaurants in a city are sampled and the regression output is given below, what can we conclude about the slope of food quality? Since we are not given the dataset, we do not have enough information to determine if the slope differs from 0. 2) The slope is 2.521 and therefore differs from 0. 3) The slope significantly differs from 0. 4) Not enough evidence was found to conclude the slope differs significantly from 0. 5) The slope is equal to 0.
the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+???? Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Hence test whether ? is significant. Give reasons for your answer. Perform the F Test making sure to state the null and alternative hypothesis. Given an interpretation of the term “R-sq” and comment on its value.
Which of the following tools is not appropriate for studying the relationship between two numerica variables? Correlation coefficient Scatter plot Historam Regression
Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Coefficients 1186 213.48 Coefficients - 130.46 294.11 Standard Error Does the sign of the coefficient for the variable safety rating make sense? 123.87 21.89 14.26 356.37 t Stat P-value 9.575 0.0000 9.752 0.0000 -9.149 0.0000 0.825 0.4128
Aa Febru The body mass index (BMI) of a person is defined to be the person's body mass divided by the square of the person's height. The article "Influences of Parameter Uncertainties within the ICRP 66 Respiratory Tract Model: Particle Deposition" (W. Bolch, E. Farfan, et al., Health Physics, 2001:378-394) states that body mass index (in kg/m2) in men aged 25-34 is lognormally distributed with parameters u = 3.215 and o = 0.157. a.Find the mean and standard deviation BMI for men aged 25-34. b.Find the standard deviation of BMI for men aged 25-34. c.Find the median BMI for men aged 25-34. d.What proportion of men aged 25-34 have a BMI less than 20? e.Find the 80th percentile of BMI for men agėd 25 -34. 04... Rext 田

We conduct a regression of size on hhinc, owner, hhsize1, hhsize2, and hhsize3. Wedo not include the constant. The regression output is reported in Table 3. Would youconclude that the home size increases with the household size? Interpret the signand magnitude of the estimated coefficients of hhsize1, hhsize2, and hhsize3
The local utility company surveys 12 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis appears below: Bill 13.45 + 4.39*Size Coefficients Estimate Std. Error (Intercept) 13.45 Size 4.39 0.54 0.2 We are 90% confident that the mean annual electric bill increases by between dollars and dollars for every additional square foot in home size. Round your answers to three decimal places and enter in increasing order.
Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Answer Coefficients 933 167.94 - 102.63 -199.18 Does the sign of the coefficient for the variable credit score make sense? Coefficients Standard Error 95.65 17.99 10.89 19.98 t Stat P-value 9.754 0.0000 9.335 0.0000 -9.424 0.0000 -9.969 0.0000 O Yes, because it is expected that as the credit score increases then the cost should decrease. O No, because it is expected that as the credit score increases then the cost should decrease. O Yes, because it is expected that as the credit score increases then the cost should also increase. O No, because it is expected that as the credit score increases then the cost should also increase. Tables Keypad Keyboard Shortcuts
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 80 mm Hg. Use a significance level of 0.05. Right Arm 100 99 93 77 77 Q Left Arm 174 168 148 148 146 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is ŷ=+x. (Round to one decimal place as needed.) mm Hg. Given that the systolic blood pressure in the right arm is 80 mm Hg, the best predicted systolic blood pressure in the left arm is (Round to one decimal place as needed.) Data table Critical Values of the Pearson Correlation Coefficient r α = 0.05 α = 0.01 0.950 0.990 0.959 0.878 0.811 0.917 0.754 0.875 0.707 0.834 0.666 0.798 0.632 0.765 0.602 0.735 0.576 0.708 0.553 0.684 0.532 0.661 0.514 0.641 0.497 0.623 0.482…
Do the following plots show 1. Constant variability 2. Nearly normal residuals 3. Independent observations for SLR (conditions for linear regression)

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