MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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- 17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…arrow_forwardA recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?arrow_forwardSuppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?arrow_forward
- Suppose that you have estimated coefficients for the regression model Y = B₁ + B₁X₁ + ß2X2 + ß3X3. Test the hypothesis that all three of the predictor variables are equal to 0, given the analysis of variance shown on the right. Use α = 0.05. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternartive hypotheses below. A. Ho: B₁ B₂ =B3 = 0 H₁: at least one ß; #0 C. Ho: B₁ B₂ = 3 = 0 H₁: B₁0, B₂0, B3 > 0 Find the critical value. The critical value is (Round to two decimal places as needed.) Source Regression Residual Error DF SS 3 9,654 23 2,400 B. Hō: at least one ß; ‡0 H₁: B₁ =B₂ =B3 = 0 D. H₁: B₁ = P₂ = ³3 = 0 H₁: B₁ B₂ B3 0 MSarrow_forwardConsider a randomized block design involving three treatments and two blocks. Define all variables. X1 X2 Treatment 1 2. 1 3 Let x, = 0 if ---Select-- v is in effect and 1 if --Select--- v is in effect. Write a multiple regression equation that can be used to analyze the data. E(y) =arrow_forwardBelow are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excelarrow_forward
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