Statistical Insights and Predictive Techniques

What is a null hypothesis in the context of statistical testing?

• A theory that there is a significant effect or relationship between variables

• A statement that there is no effect or relationship between variables

• The hypothesis that the researcher aims to prove

• A type of hypothesis that can only be used in non-parametric tests

What does a p-value indicate in hypothesis testing?

• The probability that the null hypothesis is true

• The probability of observing the data, or something more extreme, if the null hypothesis is true

• The proportion of the data that supports the alternative hypothesis

• The likelihood that the test statistic is due to chance

Which of the following correlation coefficients indicates the strongest relationship between two variables?

• -0.8

• 0.5

• -0.3

• 0.1

In simple linear regression, what does the slope of the regression line represent?

• The mean value of the response variable

• The predicted value of the response variable when the predictor is zero

• The change in the response variable for a one-unit change in the predictor

• The correlation between the predictor and the response variable

If the p-value is less than the significance level (alpha), what is the appropriate action?

• Accept the null hypothesis

• Reject the null hypothesis

• Increase the sample size

• Conduct a different test

What does it mean if two variables have a correlation coefficient close to zero?

• There is a perfect positive linear relationship between the variables

• There is a strong negative linear relationship between the variables

• There is no linear relationship between the variables

• The variables are identical

In the context of simple linear regression, what is the residual?

• The difference between the observed value and the mean of the response variable

• The average of the squared differences from the mean

• The difference between the observed value and the predicted value from the regression line

• The slope of the regression line

What is the purpose of regression analysis in exploratory data analysis?

• To classify data into different categories

• To summarize the main characteristics of the data

• To understand the relationship between variables and make predictions

• To calculate the mean and standard deviation of the data

Which of the following is a correct interpretation of a correlation coefficient of -0.9?

• There is a weak negative linear relationship between the variables

• There is a strong negative linear relationship between the variables

• There is a weak positive linear relationship between the variables

• There is a strong positive linear relationship between the variables

What assumption is made about the residuals in a simple linear regression model?

• The residuals are normally distributed

• The residuals are uniformly distributed

• The residuals are positively skewed

• The residuals are larger for larger values of the predictor