1. Regression methods were used to analyze the data from a study investigating therelationship between compressive strength (x) and intrinsic permeability (y) of variousconcrete mixes and cures. Summary quantities were n=20, E y=572, E y}=23,530,Σχ-43, Σx=157.42 and Σ x γι-1 697.80.(a) Calculate the least squares estimates of the slope and intercept.(b) Estimate o?.(c) Suppose that the observed value of permeability at x=3.5 is y=41. Calculate the valueof the corresponding residual.2. Consider the following computer output:Analysis of VarianceSourcedf SSMS F p-valueRegression1Residual error1404Total19 1500a) Find the degree of freedom for the residual error.b) What is the estimate of o??c) Calculate the F-statistic value for the regression.d) Estimate the p-value for the regression F-statistic.

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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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The large national bank charges local companies for using their services. A bank official reported the results of a regression analysi designed to predict the bank's charges (Y), measured in RM per month for services rendered to local companies. One independent variable used to predict service charge to a company is the the company's sales revenue (X), measured in millions of RM. Data for 21 companies who use the bank's services were used to fit the model. The results of the simple linear regression are provided below. Based on results below, a 95% confident interval for B is (15,30). Interpret the interval. * ŷ = -2,700 + 20X Sxy = 65, two – tailed p – value = 0.034 (for testing B We are 95% confident that the sales revenue (X) will increase between RM15 and RM30 million for every RM1 increase in service charge (Y). We are 95% confident that the mean service charge will fall between RM15 and RM30 per month. We are 95% confident that the average service charge (Y) will increase between…
Researchers found a positive assodation between the students' performance in STAT 1000 and their first-year cumulative college GPA. Furthermore, STAT 1000 course GPA explained 62% of the variation in students'first-year cumulative college GPA. The summarized data is given below: Mean STAT 1000 GPA = 25 Std. dev. - 0.21 Mean cumulative College GPA = 325 Std. dev, = 03 The slope and intercept of the least squares regression line for predicting first-year college GPA from STAT 1000 scores are, respectively. Oa Slope 055 Intercept 1.88 Ob Slope = 1.12 Intercept 1.88 Oc Slope = 1.12 Intercept 044 Od. Slope 044 Intercept 055 Oe Slope- 1.88 Intercept 055
Pipe flow in a pipe system, the 5 min interval flow speeds are measured in hydraulic testing.calculate the sum of squares of residuals (Sr=E n>i=0 e^2 i ) according to the simple linear regression model.
c) Give the expression of R˜^2 in terms of R^2 , and justify your answer.
An engineer at a company wants to model the relationship between the yield (y) and three variables: pressure (x1), volume (x2) and temperature (x3). Data is collected and the output of the statistical analysis is displayed table below. i. From appropriate statistical tests, determine the relationship between yield and the three variables, Use a 5% significance level where required.
What is the R2 value for the relationship between Height and Weight?
Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at Which of the following would linearize the data for volume and time? different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved Seconds, cm3 O In(Seconds), cm3 Seconds, In(cm') pattern. O In(Seconds), In(cm³)
A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
Find the least square regression line.
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The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is
A study was conducted in California to investigate the relationship between house size (x in square feet) and house price (y in thousands of dollars). The least-square regression line is given below y= 263.5 + 0.174x R2 = 0.728 a) Interpret the slope of the given regression line b) find the predicted house price for a house size of 120 square feet c) if the actual house price was $449.5 thousand dollars for a house size of 1200 square feet, calculate the residual of the home d) find the correlation coefficient. Round to 3 decimal places

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