## Questions and Answers

In statistical terms, what does a regression model represent?

If more than two groups have non-normal data, which test is suitable for analysis?

Which statistical test is appropriate for quantitative normally distributed data?

What is the main purpose of linear regression analysis?

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What crucial assumption does linear regression make about the errors in predictions?

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In multiple linear regression, what does Y represent?

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When is it appropriate to use a one-tail P value?

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What is the first step in performing a statistical test?

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What is the last step in performing a statistical test?

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What does a regression coefficient 𝛽=0 indicate?

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In a symmetric distribution, what percentage of cases fall within Mean ± 1 SD?

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When calculating a 95% confidence interval, what value is used for z𝛼?

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In a one-tailed test, if the other group had ended up with the smaller mean, it would be considered statistically significant.

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In a statistical test, the null hypothesis is always rejected if the P-value is less than the significance level.

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When performing a statistical test, it is essential to obtain both the test statistic and the confidence interval for accurate interpretation.

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In linear regression, a regression coefficient 𝛽=0 means that there is no association between the independent variable X and the dependent variable Y.

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The standard error (SE) of 𝛽 measures how accurately the model estimates the unknown 𝛽 and is unaffected by sample size.

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A 95% confidence interval (CI) for a point estimate 𝛽, calculated as 𝛽 ± 1.96*SE(𝛽), means that there is a 95% chance that the true value of 𝛽 falls within this interval.

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In symmetric distributions, Mean ± 3 SD includes approximately 99.7% of cases.

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In a one-tailed test, the alternative hypothesis specifies a specific direction of the effect, while the null hypothesis does not.

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When testing whether a new antibiotic impairs renal function, a left-sided one-tailed test is appropriate because it is hard to imagine a mechanism by which an antibiotic would increase the glomerular filtration rate.

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The P-value of 0.004 indicates strong evidence against the null hypothesis.

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The Mann-Whitney U-test is suitable for quantitative normally distributed data.

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Linear regression models can only represent how a dependent variable depends on one independent variable.

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A statistical model is a complex representation of reality, often involving multiple layers and variables.

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## Study Notes

- The text is from a lecture on Statistics and Data Analysis (BMS2043) at the University of Surrey during Spring 2024.
- Youngchan Kim, PhD, is the lecturer teaching inferential statistics, part 1.
- Steps to perform a statistical test: formulate null and alternative hypotheses, evaluate data and choose an appropriate statistical test, perform the test, obtain test statistic and P-value, evaluate statistical significance, and accept or reject null hypothesis.
- One-tailed test: appropriate when previous data, physical limitations, or common sense suggest the difference can only go in one direction. The alternative hypothesis must specify the predicted direction, and if the other group had a larger mean, it would be attributed to chance.
- Inferential statistics covers correlation and associated P-value, test of frequencies, quantitative normally distributed data, quantitative non-normal data, more than 2 groups, and linear regression.
- Linear regression: a method to model the relationship between a dependent variable and one or more independent variables. It identifies the line (regression model) that minimizes the sum of squared differences between observed and predicted values, using the least squares method.
- Linear regression assumes a linear relationship, normally distributed errors, and homoscedasticity.
- Multiple linear regression: models the relationship between a dependent variable and multiple independent variables. The goal is to estimate the intercept, regression coefficients, and their standard errors.
- Confidence intervals: measure the precision of an estimate by calculating the range within which the true value most likely lies, based on the sample data. For example, a 95% confidence interval would include 95.4% of all cases within ±2 standard deviations of the mean.
- One-tailed t-test: used when we have an a priori hypothesis about the direction of the difference. For example, a scientist wants to test if FTO gene variations increase BMI in Europeans.
- In another example, an antibiotic's effect on serum creatinine is tested, assuming it either does not change or increases mean serum creatinine.

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## Description

Test your knowledge of linear regression, including simple and multiple linear regression analysis techniques. Linear regression is used to create models that describe the relationship between dependent and independent variables.