In a simple linear regression based on 30 observations, it is found that b1 = 3.57 and se(b1) = 1.36. Consider the hypotheses:H0: β1 = 0 and HA: β1 ≠ 0.a. Calculate the value of the test statistic. (Round your answer to 3 decimal places.) b. Find the p-value. [Hint: The test statistic has a t-distribution with df = 30 – 2. Refer to Chapter 9 of the formula sheet to get the appropriate p-value.] p-value < 0.01 0.01 p-value < 0.02 p-value 0.10 0.05 p-value < 0.10 0.02 p-value < 0.05 c. At the 5% significance level, what is the conclusion? Is the explanatory variable statistically significant? Reject H0; the explanatory variable is significant. Reject H0; the explanatory variable is not significant. Do not reject H0; the explanatory variable is significant. Do not reject H0; the explanatory variable is not significant.
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.
In a simple linear regression based on 30 observations, it is found that b1 = 3.57 and se(b1) = 1.36. Consider the hypotheses:
H0: β1 = 0 and HA: β1 ≠ 0.
a. Calculate the value of the test statistic. (Round your answer to 3 decimal places.)
b. Find the p-value.
[Hint: The test statistic has a t-distribution with df = 30 – 2. Refer to Chapter 9 of the formula sheet to get the appropriate p-value.]
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p-value < 0.01
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0.01p-value < 0.02
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p-value0.10
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0.05p-value < 0.10
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0.02p-value < 0.05
c. At the 5% significance level, what is the conclusion? Is the explanatory variable statistically significant?
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Reject H0; the explanatory variable is significant.
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Reject H0; the explanatory variable is not significant.
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Do not reject H0; the explanatory variable is significant.
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Do not reject H0; the explanatory variable is not significant.
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