Consider the following data for a dependent variable y and two independent variables, x, and x2.X1 x2y301295471010825171125116178405945119175747170361211759131427616212The estimated regression equation for these data isý = -18.52 + 2.01x, + 4.75x2.14,109.8, 5b,= 0.2464, andHere, SST = 15,234.1, SSR == 0.9457.(a) Test for a significant relationship among x,, x,, and y. Use a = 0.05.State the null and alternative hypotheses.O Ho: B1 = 82 = 0H: One or more of the parameters is not equal to zero.O Ho: B, < B2H: B, 2 82O Ho: B, +0 and B2 = 0H: B, = 0 and B2 + 0O Ho: B1 > B2H: B, s B2O Ho: B, + 0 and 82 # 0H: One or more of the parameters is equal to zero.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 = Find the p-value. (Round your answer to three decimal places.)p-value =State your conclusion.O Do not reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.O Reject H,. Theres insufficient evidence to conclude that there is a significant relationship among the variables.O Do not reject H,. There is insufficient evidence to conclude that there is a significant relationship among the variables.(b) Is 8, significant? Use a = 0.05.State the null and alternative hypotheses.O Ho: B, = 0H: B, > 0O Ho: B1 > 0O H;: B, +0H: B = 0O H;: B, = 0H: B + 0O Họ: B1 < 0H,: B, 20Find 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.O Do not reject H,. There is insufficient evidence to conclude that 8, is significant.Reject H.. There is insufficient evidence to conclude that 8, is significant.O Reject H. There is sufficient evidence to conclude that 8, is significant.O Do not reject H,. There is sufficient evidence to conclude that 8, is significant.

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Consider the following data for a dependent variable y and two independent variables, x, and x,. X1 X2 Y 30 12 95 47 10 108 25 17 112 51 16 178 40 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 212 The estimated regression equation for these data is ý --18.52 + 2.01x, + 4.75x2. Here, SST - 15,234.1, SSR - 14,109.8, s,, - 0.2464, and s. - 0.9457. (a) Test for a significant relationship among x,, X2, and y. Use a = 0.05. State the null and alternative hypotheses. O Ho: B - P2 - 0 H,: One or more of the parameters is not equal to zero. O Ho: B1 « B2 O Ho: B, * 0 and B2 - 0 H,: B, - 0 and B, + 0 O Ho: B1 > B2 O Ho: B *0 and B2 0 H,: One or more of the parameters is equal to zero. 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.) Oavalue

Consider the following data for a dependent variable y and two independent variables, x, and x,. X1 X2 Y 30 12 95 47 10 108 25 17 112 51 16 178 40 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 212 The estimated regression equation for these data is ý --18.52 + 2.01x, + 4.75x2. Here, SST - 15,234.1, SSR - 14,109.8, s,, - 0.2464, and s. - 0.9457. (a) Test for a significant relationship among x,, X2, and y. Use a = 0.05. State the null and alternative hypotheses. O Ho: B - P2 - 0 H,: One or more of the parameters is not equal to zero. O Ho: B1 « B2 O Ho: B, * 0 and B2 - 0 H,: B, - 0 and B, + 0 O Ho: B1 > B2 O Ho: B *0 and B2 0 H,: One or more of the parameters is equal to zero. 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.) Oavalue

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Consider the following data for a dependent variable y and two independent variables, x, and x2.
X1 x2
y
30
12
95
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
212
The estimated regression equation for these data is
ý = -18.52 + 2.01x, + 4.75x2.
14,109.8, 5b,
= 0.2464, and
Here, SST = 15,234.1, SSR =
= 0.9457.
(a) Test for a significant relationship among x,, x,, and y. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B1 = 82 = 0
H: One or more of the parameters is not equal to zero.
O Ho: B, < B2
H: B, 2 82
O Ho: B, +0 and B2 = 0
H: B, = 0 and B2 + 0
O Ho: B1 > B2
H: B, s B2
O Ho: B, + 0 and 82 # 0
H: One or more of the parameters is equal to zero.
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 =

Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
O Do not reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.
O Reject H,. There is sufficient evidence to conclude that there is a significant relationship among the variables.
O Reject H,. There
s insufficient evidence to conclude that there is a significant relationship among the variables.
O Do not reject H,. There is insufficient evidence to conclude that there is a significant relationship among the variables.
(b) Is 8, significant? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B, = 0
H: B, > 0
O Ho: B1 > 0
O H;: B, +0
H: B = 0
O H;: B, = 0
H: B + 0
O Họ: B1 < 0
H,: B, 20
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.
O Do not reject H,. There is insufficient evidence to conclude that 8, is significant.
Reject H.. There is insufficient evidence to conclude that 8, is significant.
O Reject H. There is sufficient evidence to conclude that 8, is significant.
O Do not reject H,. There is sufficient evidence to conclude that 8, is significant.

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