ou may need to use the appropriate technology to answer this question. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 93 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 16 210
ou may need to use the appropriate technology to answer this question. Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 93 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 16 210
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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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
You may need to use the appropriate technology to answer this question.
Consider the following data for a dependent variable y and two independent variables,
x1
and
x2.
|
x1
|
x2
|
y |
|---|---|---|
| 30 | 12 | 93 |
| 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 | 210 |
The estimated regression equation for these data is
ŷ = −18.21 + 2.01x1 + 4.72x2.
Here, SST = 15,134.9, SSR = 13,994.6,
sb1 = 0.2482,
and
sb2 = 0.9524.
THIS PART IS C.
Is β2 significant? Use ? = 0.05.
State the null and alternative hypotheses.
- H0: β2 < 0
Ha: β2 ≥ 0H0: β2 ≠ 0
- Ha: β2 = 0 H0: β2 = 0
Ha: β2 > 0H0: β2 > 0
- Ha: β2 ≤ 0H0: β2 = 0
Ha: β2 ≠ 0
Ha: β2 ≥ 0H0: β2 ≠ 0
- Ha: β2 = 0 H0: β2 = 0
Ha: β2 > 0H0: β2 > 0
- Ha: β2 ≤ 0H0: β2 = 0
Ha: β2 ≠ 0
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.)
Conclusion:
Reject H0. There is insufficient evidence to conclude that β2 is significant.
Reject H0. There is sufficient evidence to conclude that β2 is significant.
Do not reject H0. There is insufficient evidence to conclude that β2 is significant.
Do not reject H0. There is sufficient evidence to conclude that β2 is significant.
Transcribed Image Text:(a) Test for a significant relationship among x, X3, and y. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B1 < B2
O Họ: B1 > B2
Hgi Bq S Bz
O Ho: B1 = B2 = 0
H: One or more of the parameters is not equal to zero.
O Ho: B, * 0 and B, = 0
H: B, = 0 and B, * 0
O Ho: B, * 0 and B, # 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 =
State your conclusion.
O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables.
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 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.
Transcribed Image Text:(b) Is B, significant? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B1 * 0
H: B, = 0
O Ho: B, > 0
O Ho: B1 = 0
H: B, * 0
O Ho: B1 = 0
Hi ß, > 0
O Ho: B, < 0
a'
1
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 Hp: There is sufficient evidence to conclude that B, is significant.
Do not reject H,. There is insufficient evidence to conclude that B, is significant.
Reject Ho.
There is insufficient evidence to conclude that B, is significant.
Reject Ho.
There is sufficient evidence to conclude that B, is significant.
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