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Occasionally an investigator may wish to compute a confidence interval for a, the y-intercept of the true regression line, or test hypotheses about a. The estimated y-intercept is simply the height of the estimated line when x= 0, since a + b(0) a. This implies that s, the estimated standard deviation of the statistic a, results from substituting x = 0 in the formula for 5+ bx The desired confidence interval is then at (t critical value) s, and a test statistic is a-hypothesized value t = You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) An article used the simple linear regression model to relate surface temperature as measured by a satellite (y) to actual air temperature (x) as determined from a thermocouple placed on a traversing vehicle. Selected data are given. x -2 -1 0 1 2 3 4 5 6 7 0.5 2.0 1.3 2.9 Y -3.8 -2.0 -1.9 -1.1 0.0 2.0 Estimate the population regression line. (Round your numerical values to four decimal places.) 9- (b) Compute the estimated standard deviation s. (Round your answer to four decimal places.) Carry out a test at level of significance 0.05 to see whether the y-intercept of the population regression line differs from zero. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value. (Round your answer to four decimal places.) P-value- What can you conclude?

Occasionally an investigator may wish to compute a confidence interval for a, the y-intercept of the true regression line, or test hypotheses about a. The estimated y-intercept is simply the height of the estimated line when x= 0, since a + b(0) a. This implies that s, the estimated standard deviation of the statistic a, results from substituting x = 0 in the formula for 5+ bx The desired confidence interval is then at (t critical value) s, and a test statistic is a-hypothesized value t = You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) An article used the simple linear regression model to relate surface temperature as measured by a satellite (y) to actual air temperature (x) as determined from a thermocouple placed on a traversing vehicle. Selected data are given. x -2 -1 0 1 2 3 4 5 6 7 0.5 2.0 1.3 2.9 Y -3.8 -2.0 -1.9 -1.1 0.0 2.0 Estimate the population regression line. (Round your numerical values to four decimal places.) 9- (b) Compute the estimated standard deviation s. (Round your answer to four decimal places.) Carry out a test at level of significance 0.05 to see whether the y-intercept of the population regression line differs from zero. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value. (Round your answer to four decimal places.) P-value- What can you conclude?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Occasionally an investigator may wish to compute a confidence interval for a, the y-intercept of the true regression line, or test hypotheses about a. The estimated y-intercept is simply the height of the estimated line when x= 0, since a + b(0) a. This implies that s, the estimated standard deviation of the statistic a, results from substituting x = 0 in the formula for 5+ bx The desired confidence interval is then at (t critical value) s, and a test statistic is a-hypothesized value t = You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) An article used the simple linear regression model to relate surface temperature as measured by a satellite (y) to actual air temperature (x) as determined from a thermocouple placed on a traversing vehicle. Selected data are given. x -2 -1 0 1 2 3 4 5 6 7 0.5 2.0 1.3 2.9 Y -3.8 -2.0 -1.9 -1.1 0.0 2.0 Estimate the population regression line. (Round your numerical values to four decimal places.) 9- (b) Compute the estimated standard deviation s. (Round your answer to four decimal places.) Carry out a test at level of significance 0.05 to see whether the y-intercept of the population regression line differs from zero. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value. (Round your answer to four decimal places.) P-value- What can you conclude?
Transcribed Image Text:Occasionally an investigator may wish to compute a confidence interval for a, the y-intercept of the true regression line, or test hypotheses about a. The estimated y-intercept is simply the height of the estimated line when x= 0, since a + b(0) a. This implies that s, the estimated standard deviation of the statistic a, results from substituting x = 0 in the formula for 5+ bx The desired confidence interval is then at (t critical value) s, and a test statistic is a-hypothesized value t = You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) An article used the simple linear regression model to relate surface temperature as measured by a satellite (y) to actual air temperature (x) as determined from a thermocouple placed on a traversing vehicle. Selected data are given. x -2 -1 0 1 2 3 4 5 6 7 0.5 2.0 1.3 2.9 Y -3.8 -2.0 -1.9 -1.1 0.0 2.0 Estimate the population regression line. (Round your numerical values to four decimal places.) 9- (b) Compute the estimated standard deviation s. (Round your answer to four decimal places.) Carry out a test at level of significance 0.05 to see whether the y-intercept of the population regression line differs from zero. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value. (Round your answer to four decimal places.) P-value- What can you conclude?
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