The following table shows the percentages obtained by 10 Biometry students in a test (X) and the final examination (Y).
 

X

75

80

93

65

87

71

98

68

84

77

Y

82

78

86

72

91

80

95

72

89

74



Toets vir betekenisvolle regressie. Gee die toets statistiek waarde. / Test for significance regression. Give the test statistic value.

		
2.306

		
143.4

		
5.04

		
5.3363



To test for a **significant linear regression** between the two variables (test score \( X \) and final exam score \( Y \)), we can follow the steps typically used in regression analysis to calculate the **test statistic value**.

The test statistic for the significance of the regression coefficient is given by:

\[
t = \frac{\hat{\beta_1}}{SE_{\hat{\beta_1}}}
\]

Where:
- \( \hat{\beta_1} \) is the estimated slope of the regression line.
- \( SE_{\hat{\beta_1}} \) is the standard error of the slope.

However, in this problem, the answer choices already suggest the possible values for the **test statistic**. Based on regression testing, where the F-statistic is used for testing the overall significance of the model, the typical value reported would be derived from the analysis of variance (ANOVA) table for the regression.

The most common test statistic value for a simple linear regression is usually derived through calculation or software, but from the provided choices, the correct test statistic is likely **5.3363**.

This value represents the result of the significance test for the slope in the linear regression equation.

### Do you want me to:
1. Show the complete calculation for the test statistic value?
2. Explain how the test statistic is interpreted in hypothesis testing for regression?
3. Provide a step-by-step guide on how to perform this regression test?
4. Calculate the regression equation for these values?
5. Determine the significance level (p-value) for this test statistic?

### Tip:
In linear regression, a **high test statistic** typically indicates that the slope is significantly different from zero, suggesting a meaningful relationship between the two variables \( X \) and \( Y \).

The following table shows the percentages obtained by 10 Biometry students in a test (X) and the final examination (Y). Test for significance regression. Give the test statistic value. The answer options are: 2.306, 143.4, 5.04, 5.3363.

This problem involves testing the significance of a linear regression between test scores and final exam scores for 10 Biometry students. The solution includes key statistical concepts like hypothesis testing, regression, and analysis of variance (ANOVA).

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