# 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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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
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There is a dataset of size n = 51 and is for the 50 states and the District of Columbia in the United States. The dependent variable is year 2002 birth rate per 1000 females 18 to 19 years old and independent variable is the violent crime rate (per 1000 population). A simple linear regression model is run with the results given below. What is the Pearson correlation coefficient between x and y variables? The R squared of the model? What kind of relationship there is?

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