10.Consider the following regression model:Y; = Bo + B1X1i + B2X2i + B3X3¡ + B4X4¡ + UiWe want to test the following null hypothesis:Họ: ß3+B4 = 0vs. H1: B3+B4 # 0%3DThe initial regression, so that the null hypothesis can be tested using the t-statistic method(testing a restriction on a single regression coefficient), can be rewritten using the followingform:Y; = Bo + B1X11 + B2X2¡ + Y1X3¡ + B4W; + u;where W; can be calculated from the data.Here, yı.-Вз + Ba. Here, W,X3i + X4i.A)+, ==, ==, +

Consider the following regression model: Y; = Bo + B1X1i + B2X2¡ + B3X3¡ + B4X4¡ + Ui We want to test the following null hypothesis: Họ: ß3+ß4 = 0 vs. H1: B3+ß4 # 0 The initial regression, so that the null hypothesis can be tested using the t-statistic m (testing a restriction on a single regression coefficient), can be rewritten using the fo form:

Consider the following regression model: Y; = Bo + B1X1i + B2X2¡ + B3X3¡ + B4X4¡ + Ui We want to test the following null hypothesis: Họ: ß3+ß4 = 0 vs. H1: B3+ß4 # 0 The initial regression, so that the null hypothesis can be tested using the t-statistic m (testing a restriction on a single regression coefficient), can be rewritten using the fo form:

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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In a data set with 12 observations, you try fitting two regression models. The esti-mated models are summarized as: Model 1: Y(hat) =3.5 + 2x; SSR= 5, and SSE= 10;Model 2: Y(hat) =3.0 + 1.5x + 0.4^2; SSR=23, and SSE=7 (a) Calculate R2 for both models. b. for both models test the null hypothesis that all the regression coefficients other than the intercept are 0.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents. xx 11.5 8.5 6.7 3.5 2.9 2.7 2.7 0.9 yy 14.1 11 10 7.3 6.7 6.4 6.4 4.7 Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. Round to 2 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 10.2 thousand automatic weapons? Round to 3 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 5.8 thousand automatic weapons? Round to 3 decimal places.
In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats' diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:ŷ = 36 + .8x1 − 1.7x2Also provided are SSR = 60 and SST = 180.The test statistic for testing the significance of the model is _____. a. 5.00 b. .50 c. .25 d. .33
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Use the following results obtained from a simple linear regression analysis with 12 observations. Y = 37.2895- (1.2024)X Sb = 0.2934 Test to determine if there is a significant negative relationship between the independent and dependent variables at alpha= .05. Give the resulting conclusion. a. is rejected. B.cannot be tested with the given information. c. is not rejected. D. is not an appropriate null hypothesis for this situation.
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Consider the following two a.m. peak work trip generation models, estimated by household linear regression: T = 0.62 + 3.1 X1 + 1.4 X2 R2= 0.590 (2.3) (7.1) (5.9) T = 0.01 + 2.4 X1 + 1.2 Z1 + 4.0 Z2 R2= 0.598 (0.8) (4.2) (1.7) (3.1) X1 = number of workers in the household X2 = number of cars in the household, Z1 is a dummy variable which takes the value 1 if the household has one car, Z2 is a dummy variable which takes the value 1 if the household has two or more cars. Compare the two models and choose the best. If a zone has 1000 households, of which 50% have no car, 35% have one car, and the rest have exactly two cars, estimate the total number of trips generated by this zone. Use the preferred trip generation model and assume that each household has an average of two workers