You may need to use the appropriate technology to answer this question. Consider the data. xi 3 12 6 20 14 yi 70 40 55 5 10 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi − x)2. (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (α = 0.05): H0: β1 = 0 Ha: β1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between x and y is significant.Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant. (e) Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant. Do not reject H0. We cannot conclude that the relationship between x and y is significant.Reject H0. We conclude that the relationship between x and y is significant.

You may need to use the appropriate technology to answer this question. Consider the data. xi 3 12 6 20 14 yi 70 40 55 5 10 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi − x)2. (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (α = 0.05): H0: β1 = 0 Ha: β1 ≠ 0 Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between x and y is significant.Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant. (e) Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Do not reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant. Do not reject H0. We cannot conclude that the relationship between x and y is significant.Reject H0. We conclude that the relationship between x and y is significant.

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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Question

You may need to use the appropriate technology to answer this question.

Consider the data.

x_i	3	12	6	20	14
y_i	70	40	55	5	10

(a)

Compute the mean square error using equation

s² = MSE =

SSE

n − 2

(Round your answer to two decimal places.)

(b)

Compute the standard error of the estimate using equation

s =

MSE

SSE

n − 2

(Round your answer to three decimal places.)

(c)

Compute the estimated standard deviation of

b₁

using equation

s_b1 =

Σ(x_i − x)²

(Round your answer to three decimal places.)

(d)

Use the t test to test the following hypotheses (α = 0.05):

H₀:	β₁	=	0
H_a:	β₁	≠	0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We conclude that the relationship between x and y is significant.Do not reject H₀. We cannot conclude that the relationship between x and y is significant. Reject H₀. We conclude that the relationship between x and y is significant.Reject H₀. We cannot conclude that the relationship between x and y is significant.

(e)

Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.

Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Regression
Error
Total

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We conclude that the relationship between x and y is significant.Reject H₀. We cannot conclude that the relationship between x and y is significant. Do not reject H₀. We cannot conclude that the relationship between x and y is significant.Reject H₀. We conclude that the relationship between x and y is significant.

(e) Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)
Source
Sum
Degrees
of Freedom
Mean
of Variation
of Squares
Square
F
p-value
Regression
1
2531.25
2531.25
0.019
3
348.75
116.25
Error
Total
4
2880
Find the value of the test statistic. (Round your answer to two decimal places.)
21.77
Find the p-value. (Round your answer to three decimal places.)
p-value = 0.019
State your conclusion.
O Do not reject H,. We conclude that the relationship between x and y is significant.
O Reject Ho. We cannot conclude that the relationship between x and y is significant.
O Do not reject H,. We cannot conclude that the relationship between x and y is significant.
O Reject Ho. We conclude that the relationship between x and y is significant.

Consider the data.
X;
3
12
6
20
14
70
40
55
5
10
SSE
(a) Compute the mean square error using equation s = MSE =
n -
(Round your answer to two decimal places.)
1613.33
SSE
(b) Compute the standard error of the estimate using equation s = MSE =
(Round your answer to three decimal places.)
n - 2
40.166
(c) Compute the estimated standard deviation of b, using equation s,
(Round your answer to three decimal places.)
V E(x;
1.603
(d) Use the t test to test the following hypotheses (a = 0.05):
Hoiß = 0
Find the value of the test statistic. (Round your answer to three decimal places.)
0.285
Find the p-value. (Round your answer to four decimal places.)
p-value = 0.3971
State your conclusion.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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