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The ANOVA summary table to the right is for a mulfiple regressian model with three indoperident. variables. Complele parts (a) through (e) a. Determine the regression mean square (MSR) and the mean square error (MSE) MSR=(Roundtofourdecimalplacesasnoeded.)MSE= (Roundtofourdecimalplacesasneeded.) b. Compute the cverali Fitht test itabsic. FITAT STA (Round to two decimal places as needed.) c. Determine whether there is a signiticant relationstip between Y and the three independent variables at the 0.05 level of sign State the null and atternative hypotheses. Choose the correct hypotheses below A. H0f1m2=P3=0 B. H.1=2=3=0 A1: 1=2=p2=0 Hy: Ar least one f A C. H3;1=2=3=0 D. Ho 1+2+p3+0 H1 At least one f=0, for j=1,2,3 A4 :1=2=3=0The ANOVA summayy table to the right is for a multiple regression model with three independent variables, Complete parts (a) through (e) H1 At least one =0, lor j=1,2,3 vortirasr3=:H 1=1=2=3=0 The p-value is (Round to three decimal places as needed) Draw a conclusion. Choose the correct answer below. A. There is insufficient evidence of a significant linear relationskip with at least one of the independent variables because the p-valuo is greater than the level of aignificance. 8. There is mufficient evidence of a significant linear relatienship with at least one of the independent variables because the test statistic is greater than the critical value. C. There is sutficient evidence of a significant linear relationship wet at least one of the independent variables because the test statistic is less than the critical value. D. There is insulficient evidence of a signifant inear relatgnship with at least one of the independent variables because the test statistic is less than the level of significance. d. Compute the coeficient of maltiple determination, r2, and interpeet its meaning r2= (Round to four decimal places as needed.) Interpret the meaning of the coefficient of mutiple determination The coetficient of muliple determination indicates that W of the variation in the variable can be explained by the varation in the (Round to two decimal places as needed.) e. Compule the adjusted r2..

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BUS 305: SOLUTIONS TO PRACTICE PROBLEMS EXAM 2 1) B 2) B 3) No, fan pattern (heteroscedasticity) 4) No, nonlinear relationship between X and Y 5) The black line is the regression line because it get closest to the sample points (minimizes error between the points and the line). The red line has a larger error; that is, larger total distance from points to the line. 6) Because it is reasonable to suppose that costs are dependent on production volume (since units are produced, directly resulting in costs), then regression is more appropriate for this data since regression is appropriate when an cause-and-effect relationship is assumed. 7) C 8) a) r = 0.8; b) T = 1.31; c) p = 0.117 d) There is no evidence of a significant correlation between X and Y in the population because we did not reject the null of H0: = 0. 9) Note: the following are not complete answers to Question 11; they are just enough for you to know whether your short answer addressed the correct things. a) 1 = population slope, b1 = sample slope. On exam, would also want to address what you know (or don’t know) about each of these and how each is found. b) An outlier can “drag” the regression line toward it. On the exam, also think about how this would affect the quality of your regression model and the predictions. 10) Yes, there appears to be a straight line relationship between the variables. Linear regression appears to be appropriate. The regression output is: 11) a) T = -0.09, p = 0.929, do not reject Ho, conclude there is no evidence of a relationship b) R2 = 0.002 = 0.2%, No because value is very close to zero c) Correlation = r = -0.0421. No, there is not a strong relationship between these variables. The correlation is nearly 0. d) Regression line is Y^ = 1.26 – 0.035X. Y^ = 1.26 – 0.035(100) = 1.26 – 3.5 = -2.24. No this does not make sense because you cannot have a negative number of near misses. It is not wise to predict with this model. The R-squared value is extremely low (essentially 0%), which means that there is no relationship at all between near misses and flights in this data. Therefore, predicting misses from flights is meaningless. e) b1 = -0.035. As Number of flights increases by 1, we expect number of near misses to go down by 0.035. Or, put another way, as flights increases by 1000, we expect number of near misses to go down by 35. No, this does not make sense. We would assume that as flights increase, so would near misses. 12) a. Multiple regression is a direct extension of simple regression, except that now we have more than one independent (X) variable. b. Note: the following is not a complete answer; it is just enough for you to know whether your short answer addressed the correct things: Multicollinearity is when the independent variables are highly correlated with one another. On the exam, also indicate how this affects the model, how one can identify if it is present, and what can be done to correct it. c. Dummy variables are us ...

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Page 1 of 18 Part A: Multiple Choice (1–11) ______1. Using the “eyeball” method, the regression line = 2+2x has been fitted to the data points (x = 2, y = 1), (x = 3, y = 8), and (x = 4, y = 7). The sum of the squared residuals will be a. 7 b. 19 c. 34 d. 8 ______2. A computer statistical package has included the following quantities in its output: SST = 50, SSR = 35, and SSE = 15. How much of the variation in y is explained by the regression equation? a. 49% b. 70% c. 35% d. 15% ______3. In testing the significance of b, the null hypothesis is generally that a. β = b b. β 0 c. β = 0 d. β = r ______4. Testing whether the slope of the population regression line could be zero is equivalent to testing whether the population _____________ could be zero. a. standard error of estimate c. y-intercept b. prediction interval d. coefficient of correlation ______5. A multiple regression equation includes 4 independent variables, and the coefficient of multiple determination is 0.64. How much of the variation in y is explained by the regression equation? a. 80% b. 16% c. 32% d. 64% ______6. A multiple regression analysis results in the following values for the sum-of-squares terms: SST = 50.0, SSR = 35.0, and SSE = 15.0. The coefficient of multiple determination will be a. = 0.35 b. = 0.30 c. = 0.70 d. = 0.50 ______7. In testing the overall significance of a multiple regression equation in which there are three independent variables, the null hypothesis is a. : b. : c. : d. : ______8. In a multiple regression analysis involving 25 data points and 4 independent variables, the sum-of-squares terms are calculated as SSR = 120, SSE = 80, and SST = 200. In testing the overall significance of the regression equation, the calculated value of the test statistic will be a. F = 1.5 c. F = 5.5 b. F = 2.5 d. F = 7.5 ______9. For a set of 15 data points, a computer statistical package has found the multiple regression equation to be = -23 + 20+ 5 + 25 and has listed the t-ratio for testing the significance of each partial regression coefficient. Using the 0.05 level in testing whether = 20 differs significantly from zero, the critical t values will be a. t = -1.960 and t= +1.960 b. t = -2.132 and t = +2.132 c. t = -2.201 and t = +2.201 d. t = -1.796 and t = +1.796 ______10. Computer analyses typically provide a p-Value for each partial regression coefficient. In the case of , this is the probability that a. = 0 b. = c. the absolute value of could be this large if = 0 d. the absolute value of could be this large if 1 ______11. In the multiple regression equation, = 20,000 + 0.05+ 4500 , is the estimated household income, is the amount of life insurance held by the head of the household, and is a dummy variable ( = 1 if the family owns mutual funds, 0 if it doesn’t). The interpretation of = 4500 is that a. owing mutual funds increases the estimated income by $4500 b. the average value of a mut.

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Photos from our Spring Gala 2024. Thank you for making our 2024 Spring Gala unforgettable! Whether you attended or supported us with a donation, we extend our heartfelt thanks for celebrating School-Community Partnerships alongside ExpandED Schools. Special appreciation to our honorees, Rachel Skaistis and Cravath, Swaine, & Moore LLP, for their unwavering support in advancing educational equity. Your contributions have profoundly impacted countless young New Yorkers, and we’re proud to have you as part of our community. Our gratitude also extends to our Board of Directors, sponsors, city partners, community-based organizations, and the inspiring young people who joined us. Your support fuels our mission, and we’re endlessly thankful for your dedication. While we celebrate our gala’s success, our work continues. As you view the evening’s highlights, consider how you can further empower young New Yorkers and educators with your donation, no matter the size. Donate today: https://www.expandedschools.org/support-our-work/donate/

Spring gala 2024 photo slideshow - Celebrating School-Community Partnerships

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e-Sealing at EADTU by Kamakshi Rajagopal

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The ANOVA summary table to the right is for a mulfiple regre.pdf

1. The ANOVA summary table to the right is for a mulfiple regressian model with three indoperident. variables. Complele parts (a) through (e) a. Determine the regression mean square (MSR) and the mean square error (MSE) MSR=(Roundtofourdecimalplacesasnoeded.)MSE= (Roundtofourdecimalplacesasneeded.) b. Compute the cverali Fitht test itabsic. FITAT STA (Round to two decimal places as needed.) c. Determine whether there is a signiticant relationstip between Y and the three independent variables at the 0.05 level of sign State the null and atternative hypotheses. Choose the correct hypotheses below A. H0f1m2=P3=0 B. H.1=2=3=0 A1: 1=2=p2=0 Hy: Ar least one f A C. H3;1=2=3=0 D. Ho 1+2+p3+0 H1 At least one f=0, for j=1,2,3 A4 :1=2=3=0The ANOVA summayy table to the right is for a multiple regression model with three independent variables, Complete parts (a) through (e) H1 At least one =0, lor j=1,2,3 vortirasr3=:H 1=1=2=3=0 The p-value is (Round to three decimal places as needed) Draw a conclusion. Choose the correct answer below. A. There is insufficient evidence of a significant linear relationskip with at least one of the independent variables because the p-valuo is greater than the level of aignificance. 8. There is mufficient evidence of a significant linear relatienship with at least one of the independent variables because the test statistic is greater than the critical value. C. There is sutficient evidence of a significant linear relationship wet at least one of the independent variables because the test statistic is less than the critical value. D. There is insulficient evidence of a signifant inear relatgnship with at least one of the independent variables because the test statistic is less than the level of significance. d. Compute the coeficient of maltiple determination, r2, and interpeet its meaning r2= (Round to four decimal places as needed.) Interpret the meaning of the coefficient of mutiple determination The coetficient of muliple determination indicates that W of the variation in the variable can be explained by the varation in the (Round to two decimal places as needed.) e. Compule the adjusted r2.

The ANOVA summary table to the right is for a mulfiple regre.pdf

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