In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. R2 0.202 Std. Error 6.816 n 35 ANOVA table Source SS df MS F p-value Regression 387.6959 1 387.6959 8.35 .0068 Residual 1,533.0614 33 46.4564 Total 1,920.7573 34 Regression output confidence interval variables coefficients std. error t Stat p-value Lower 95% Upper 95% Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331 Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584 (a) Write the fitted regression equation. YˆY^ = + X (b-1) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (Round t.025 to 3 decimal places.) Degrees of freedom t.025 (b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠ 0. Reject the null hypothesis if tcalc > 2.035 or if tcalc < -2.035 Reject the null hypothesis if tcalc < -2.035 or if tcalc > -2.035 (c-1) Calculate t. (Round your answer to 3 decimal places.) tcalc (c-2) We reject the null hypothesis. Yes No (d-1) Find the 95% confidence interval for slope. (Round your answers to 4 decimal places.) Confidence interval is from to (d-2) The confidence interval does not contain zero, which implies there is no relationship between weekly pay and income tax withheld. there is a relationship between weekly pay and income tax withheld. (e) Calculate t2 and F. (Round your answers to 2 decimal places.) t2 Fcalc (f-1) Calculate R2. (Round your answer to 3 decimal places.) R2 (f-2) What is the percentage of variation in income tax withheld explained by weekly pay? (Round your answer to the nearest whole number.) Percentage of variation %

In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees. R2 0.202 Std. Error 6.816 n 35 ANOVA table Source SS df MS F p-value Regression 387.6959 1 387.6959 8.35 .0068 Residual 1,533.0614 33 46.4564 Total 1,920.7573 34 Regression output confidence interval variables coefficients std. error t Stat p-value Lower 95% Upper 95% Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331 Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584 (a) Write the fitted regression equation. YˆY^ = + X (b-1) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (Round t.025 to 3 decimal places.) Degrees of freedom t.025 (b-2) Choose the correct option for H0: β1 = 0 vs H1: β1 ≠ 0. Reject the null hypothesis if tcalc > 2.035 or if tcalc < -2.035 Reject the null hypothesis if tcalc < -2.035 or if tcalc > -2.035 (c-1) Calculate t. (Round your answer to 3 decimal places.) tcalc (c-2) We reject the null hypothesis. Yes No (d-1) Find the 95% confidence interval for slope. (Round your answers to 4 decimal places.) Confidence interval is from to (d-2) The confidence interval does not contain zero, which implies there is no relationship between weekly pay and income tax withheld. there is a relationship between weekly pay and income tax withheld. (e) Calculate t2 and F. (Round your answers to 2 decimal places.) t2 Fcalc (f-1) Calculate R2. (Round your answer to 3 decimal places.) R2 (f-2) What is the percentage of variation in income tax withheld explained by weekly pay? (Round your answer to the nearest whole number.) Percentage of variation %

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 the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald's employees.


R²	0.202
Std. Error	6.816
n	35

ANOVA table
Source	SS	df	MS	F	p-value
Regression		387.6959			1	387.6959	8.35	.0068
Residual		1,533.0614			33	46.4564
Total		1,920.7573			34

Regression output	confidence interval
variables	coefficients	std. error	t Stat	p-value	Lower 95%	Upper 95%
Intercept		30.7963			6.4078		4.806	.0000	17.7595	43.8331
Slope		0.0343			0.0119		2.889	.0068	0.0101	0.0584

(a) Write the fitted regression equation.

YˆY^ =  +  X

(b-1) State the degrees of freedom for a two-tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (Round t_.025 to 3 decimal places.)

Degrees of freedom
t_.025

(b-2) Choose the correct option for H₀: β₁ = 0 vs H₁: β₁ ≠ 0.

Reject the null hypothesis if t_calc > 2.035 or if t_calc < -2.035
Reject the null hypothesis if t_calc < -2.035 or if t_calc > -2.035

(c-1) Calculate t. (Round your answer to 3 decimal places.)

t_calc

(c-2) We reject the null hypothesis.

(d-1) Find the 95% confidence interval for slope. (Round your answers to 4 decimal places.)

Confidence interval is from    to

(d-2) The confidence interval does not contain zero, which implies

there is no relationship between weekly pay and income tax withheld.
there is a relationship between weekly pay and income tax withheld.

(e) Calculate t² and F. (Round your answers to 2 decimal places.)

t²
F_calc

(f-1) Calculate R². (Round your answer to 3 decimal places.)

R²

(f-2) What is the percentage of variation in income tax withheld explained by weekly pay? (Round your answer to the nearest whole number.)

Percentage of variation  %

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