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**From Statistics 1**

- Interpret diagrams for single-variable data, including an understanding that an area in a histogram represents the frequency
- Connect grouped frequency tables to probability distributions
- Interpret scatter diagrams and regression lines for bivariate data, including recognition of scatter diagrams which include distinct sections of the population
- Understand informal interpretation of correlation
- Understand that correlation does not imply causation
- Be able to calculate standard deviation, including from summary statistics
- Recognise and interpret possible outliers in data sets and statistical diagrams
- Be able to clean data, including dealing with missing data, errors and outliers

**Correlation**:

**Coefficient Calculation**: Calculate and interpret the product-moment correlation coefficient (Pearson’s*r*).**Causation vs. Correlation**: Understand the difference between causation and correlation, and the dangers of concluding based solely on correlation.

**Regression**:

**Linear Regression**:- Understand the principles behind linear regression to model relationships between two variables.
- Calculate the equation of the regression line of
*y*on*x*. - Interpret the gradient and y-intercept of the regression line in context.
- Use the regression line to make predictions and understand the limitations of extrapolation.

**Exponential Models via Logarithmic Transformation**:- Identify when data appears to fit an exponential model.
- Understand how to transform the exponential model
*y*=*ab*or^{x}*y*=*ax*using logarithms to achieve a linear form.^{b} - Perform a logarithmic transformation and plot the transformed data.
- For the transformed data, calculate the linear regression line.
- Reverse-transform the linear regression equation back to its exponential form.

**Correlation Hypothesis Testing**:

**Hypotheses Formulation**: Formulate the null and alternative hypotheses for correlation testing.**Critical Value**: Use statistical tables or technology to determine critical values for a given significance level.**Conduct Test**: Perform a hypothesis test to ascertain the significance of the correlation between two variables, given a dataset.**Results Interpretation**: Analyze and interpret the results of the hypothesis test in context.

**Correlation**:

**Coefficient Calculation**:- Introduce the formula for Pearson’s
*r*. - Provide worked examples of its calculation.

- Introduce the formula for Pearson’s
**Causation vs. Correlation**:- Discuss real-world examples where correlation does not imply causation.
- Emphasize the importance of external factors and confounding variables.

**Regression**:

**Linear Regression**:- Define the terms “gradient” and “y-intercept.”
- Derive and explain the formula for linear regression.
- Provide exercises that involve making predictions based on a regression line.

**Exponential Models via Logarithmic Transformation**:- Introduce the properties of logarithms and their application to data transformation.
- Demonstrate the transformation of exponential models to linear models.
- Provide examples of reverse transformation to retrieve the exponential model after regression analysis on transformed data.

**Correlation Hypothesis Testing**:

**Hypotheses Formulation**:- Define the null hypothesis (
*H*_{0}) and alternative hypothesis (*H*_{1}). - Discuss scenarios where one would want to test the significance of a correlation.

- Define the null hypothesis (
**Critical Value**:- Show students how to find critical values using statistical tables.
- Introduce how calculators can aid in this process.

**Conduct Test**:- Walk through the steps of conducting a hypothesis test, emphasizing the importance of each step.
- Offer varied examples and practice problems for students to try.

**Results Interpretation**:- Discuss the potential outcomes of a hypothesis test and their implications.

**Correlation**:

**All Correlation is Causation**: Students often believe that if two variables are correlated, one must cause the other.**Strength of Correlation**: Students might think a correlation coefficient of*r*=0.5 means one variable is “half caused” by the other.**Perfect Correlation**: Some believe that a correlation coefficient of exactly 1 or -1 means the data points fall perfectly on a straight line.

**Regression**:

**Extrapolation**: Students might believe that a regression model is equally accurate everywhere, even beyond the range of observed data.**Intercept Significance**: The y-intercept always has real-world significance.**Linearity Assumption**: Linear regression is suitable for all types of data distributions.**Transformed Regression**: After transforming exponential data to linear form using logarithms and creating a linear model, the data is now “linear”.

**Correlation Hypothesis Testing**:

**Significance = Importance**: A statistically significant result means the finding has practical or real-world significance.**P-value Misunderstanding**: A p-value represents the probability that the null hypothesis is true.

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