In a regression analysis involving 27 observations, the following estimated regression equation was developed:\[\hat{y} = 25.2 + 5.5x_1\]For this estimated regression equation, SST \( = 1,600 \) and SSE \( = 510 \).### (a) At \( \alpha = 0.05 \), test whether \( x_1 \) is significant.**State the null and alternative hypotheses.**- \( H_0: \beta_1 = 0 \) \( H_a: \beta_1 \neq 0 \) **Find the value of the test statistic.** (Round your answer to two decimal places.)\[ F = \underline{\hspace{3cm}} \]**Find the \( p \)-value.** (Round your answer to three decimal places.)\[ p\text{-value} = \underline{\hspace{3cm}} \]**Is \( x_1 \) significant?**- ○ Reject \( H_0 \). We conclude that \( x_1 \) is significant.- ○ Reject \( H_0 \). We conclude that \( x_1 \) is not significant.- ○ Do not reject \( H_0 \). We conclude that \( x_1 \) is significant.- ○ Do not reject \( H_0 \). We conclude that \( x_1 \) is not significant.Suppose that variables \( x_2 \) and \( x_3 \) are added to the model, and the following regression equation is obtained:\[\hat{y} = 16.3 + 2.3x_1 + 12.1x_2 - 5.8x_3\]For this estimated regression equation SST \( = 1,600 \) and SSE \( = 100 \). Use an F test and a 0.05 level of significance to determine whether \( x_2 \) and \( x_3 \) contribute significantly to the model.State the null and alternative hypotheses.- \( H_0: \beta_1 = 0 \) \( H_a: \beta_1 \neq 0 \)- \( H_0: \beta_1 \neq 0 \) \( H_a: \beta_1 = 0 \)- \( H_0: \) One or more of the parameters is not equal to zero. \( H_a: \beta_2 = \beta_3 = 0 \)- \( H_0: \beta_2 = \beta_3 = 0 \) \( H_a: \) One or more of the parameters is not equal to zero.Find the value of the test statistic. \[ \text{Value} = \_\_\_\_\_\_\_\_ \]Find the \( p \)-value. (Round your answer to three decimal places.) \[ p\text{-value} = \_\_\_\_\_ \]Is the addition of \( x_2 \) and \( x_3 \) significant?- Do not reject \( H_0 \). We conclude that the addition of variables \( x_2 \) and \( x_3 \) is significant.- Reject \( H_0 \). We conclude that the addition of variables \( x_2 \) and \( x_3 \) is not significant.- Reject \( H_0 \). We conclude that the addition of variables \( x_2 \) and \( x_3 \) is significant.- Do not reject \( H_0 \). We conclude that the addition of variables \( x_2 \) and \( x_3 \) is not significant.

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Answered: In a regression analysis involving 27…

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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A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 7; Mx = 3 What is b equal to (Please include the sign: e.g., -20)? What is a equal to (please include the sign: e.g., +4.0)? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
Use the given data to find the best predicted value. If the prediction is unreliable, state so. 5) Eight pairs of data yield r = 0.742 and the regression equation y = 55.8 + 2.79x. Also, y = 71.125. What is the best predicted value of y for x = 8? Round to one decimal place.
A regression was run to determine if there is a relationship between hours of study per week (x) and the final exam scores (y). The results of the regression were: y=ax+b a=5.865 b=25.06 r²=0.81 r=0.9 Use this to predict the final exam score of a student who studies 4.5 hours per week, and please round your answer to a whole number.
A regression was run to determine if there is a relationship between hours of study per week (X) and the test scores (y ). The results of the regression were:y=ax+ba=5.931b=20.1r2=0.748225r=0.865Use this to predict the final exam score of a student who studies 3 hours per week, and please round your answer to a whole number.
Data from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 90 mm Hg. Use a significance level of 0.05. Right Arm 101 100 92 75 75 O Left Arm 174 167 181 149 147 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is y = + x. (Round to one decimal place as needed.) Given that the systolic blood pressure in the right arm is 90 mm Hg, the best predicted systolic blood pressure in the left arm is mm Hg. (Round to one decimal place as needed.)
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 80 mm Hg. Use a significance level of 0.05. Right Arm 100 99 93 77 77 Q Left Arm 174 168 148 148 146 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is ŷ=+x. (Round to one decimal place as needed.) mm Hg. Given that the systolic blood pressure in the right arm is 80 mm Hg, the best predicted systolic blood pressure in the left arm is (Round to one decimal place as needed.) Data table Critical Values of the Pearson Correlation Coefficient r α = 0.05 α = 0.01 0.950 0.990 0.959 0.878 0.811 0.917 0.754 0.875 0.707 0.834 0.666 0.798 0.632 0.765 0.602 0.735 0.576 0.708 0.553 0.684 0.532 0.661 0.514 0.641 0.497 0.623 0.482…
An automobile rental company wants to predict the yearly maintenance expense (Y) for an automobile using the number of miles driven during the year () and the age of the car (, in years) at the beginning of the year. The company has gathered the data on 10 automobiles and run a regression analysis with the results shown below:. Summary measures Multiple R 0.9689 R-Square 0.9387 Adj R-Square 0.9212 StErr of Estimate 72.218 Regression coefficients Coefficient Std Err t-value p-value Constant 33.796 48.181 0.7014 0.5057 Miles Driven 0.0549 0.0191 2.8666 0.0241 Age of car 21.467 20.573 1.0434 0.3314 Use the information above to estimate the annual maintenance expense for a 10 years old car with 60,000 miles.
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 90 mm Hg. Use a significance level of 0.05. Right Arm 101 100 92 77 77 Left Arm 174 169 145 146 146
A regression was run to determine if there is a relationship between hours of study per week (xx) and the final exam scores (yy).The results of the regression were: y=ax+b a=5.614 b=32.79 r2=0.808201 r=0.899 Use this to predict the final exam score of a student who studies 1 hours per week, and please round your answer to a whole number.

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