# 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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A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 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.
Define Residuals or errors in Alternative Regression Models?
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e) Perform the F Test making sure to state the null and alternative hypothesis.
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
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A researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+BOIL+YEXP+8FDI Where FR = yearly foreign reserves (S000'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: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 ЕXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 S = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 3 1991.31 663.77 ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values **', **", '?'and ??"

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