Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 14.2, Problem 33E
To determine
Verify the regression
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Use the table below:
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X2
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(i) Fit a regression equation to the multiple regression model
by least squares method.
(ii) Predict Y when X1=3.5 and X2=5.5
(iii) Compute TSS, ESS and RSS.
(iv) Test for the significance of overall regression at 5% level of significance.
Consider an estimated linear regression model with a response Y and 4 predictors X1, X2, X3, X4. For a random sample of 25 observations on the response and the 4 predictors, the following estimates are obtained using Excel.
Regression Statistics
Multiple R
0.859825564
Standard Error
127.606
What is the adjusted R-square of the fitted model?
A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21
Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.
Chapter 14 Solutions
Introduction To Statistics And Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - When Coastal power stations take in large amounts...Ch. 14.3 - Prob. 39ECh. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
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- Given below are five observations collected in a regression study on two variables, x(independent variable) y, ( dependent variable). x y 11 8 21 41 31 5 51 2 Develope the least squares estimated regression equation Compute the coefficient of determination and the coefficient of correlationarrow_forwardInterpret the estimated regression coefficient corresponding to the Z variable. Data Salary Education Experience Sex 29.7985 15 3 1 21.8219 4 0 0 22.8978 4 0 0 22.0917 1 1 0 21.8993 5 0 0 22.4829 3 1 1 28.0772 15 0 0 y=salary 23.6292 6 1 1 x1=education level in schooling years 32.3595 0 15 1 x2=experience level in employment level 21.794 1 0 0 d=sex (1 for male,0 for female) 19.8762 3 0 0 Ln(Y) = alpha +beta1X1 +Beta2X2+ Beta3D +Beta4Z +e 21.0253 3 0 0 where z =X2D 24.6323 0 5 1 19.0247 0 0 0 18.8857 0 0 0 21.8552 1 0 0 24.2675 6 1 0 18.7931 0 0 0 18.9276 0 0 0 23.4441 5 1 1 20.8047 2 0 0 18.26 0 0 0 20.6726 0 2 1 21.7815 3 0 0…arrow_forwardCompute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y -intercept to at least four decimal places. =x8.2 =sx3 =y1350 =sy13,000 =r0.40arrow_forward
- In exercise 1, the following estimated regression equation based on 10 observations waspresented. y^= 29.1270 + .5906x1 + .4980x2Here SST =6724.125, SSR =6216.375, Sb1 = .0813, and Sb2 = .0567.a. Compute MSR and MSE.b. Compute F and perform the appropriate F test. Use α .05.c. Perform a t test for the significance of B1. Use α .05.d. Perform a t test for the significance of B2. Use α .05.arrow_forwardYears of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methodsarrow_forwarda) Calculate the least square regression line for X on Y of the given data?b) Calculate the coefficient of correlation of the given date? Interpret the value of the coefficient?arrow_forward
- Given below are five observations collected in a regression study on two variables, x (independent variable) and y (dependent variable).x y2 43 44 35 26 1a. Develop the least squares estimated regression equation.b. Compute the coefficient of determination.c. Compute the coefficient of correlation.arrow_forwardIn a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?arrow_forwardWhich of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2arrow_forward
- In exercise 1, the following estimated regression equation based on 10 observations was presented. y^=29.1270+.5906x1+.4980x2Develop a point estimate of the mean value of y when x1=180 and x2=310. Predict an individual value of y when x1=180 and x2=310.arrow_forwardThe accompanying data file contains 40 observations on the response variable y along with the predictor variables x1 and x2. Use the holdout method to compare the predictability of the linear model with the exponential model using the first 30 observations for training and the remaining 10 observations for validation. y x1 x2 533.86 20 30 104.84 15 20 64.89 20 23 159.61 16 21 43.06 13 16 4.27 13 13 736.56 15 30 64.89 20 23 10.64 20 22 76.90 18 20 4.89 11 13 80.90 11 16 224.17 12 19 45.75 16 25 8.13 17 17 319.97 13 30 48.61 19 25 564.67 12 27 111.87 11 25 152.39 13 24 13.34 18 14 28.80 15 22 37.56 13 15 105.62 17 26 44.05 18 21 451.65 17 28 10.34 18 21 32.70 12 13 19.21 14 12 14.02 15 16 2.45 16 12 2.48 20 15 50.34 17 21 29.31 17 20 33.75 16 12 196.28 17 29 943.12 13 30 7.25 10 12 89.73 15 25 32.91 12 18 1. Use the training set to estimate Models 1 and 2. Note: Negative values should be indicated by a…arrow_forwardA student used multiple regression analysis to study how family spending (y) is influenced by income(x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousandsof dollars. The following results were obtained.ANOVAdf SSRegression 3 45.9634Residual 11 2.6218TotalCoefficients Standard ErrorIntercept 0.0136x10.7992 0.074x20.2280 0.190x3-0.5796 0.920 Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.arrow_forward
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