Conduct a regression analysis for the following data.

Q2.1 Test the hypothesis that X is a good predictor of Y and explain why or why not. (3 points)

Q2.2 Explain the various parameters of the linear equation. (5 points)

Q2.3 Explain the strength of the model using the regression model and also using a correlation analysis. (5 points)

Q2.4 Show the linear line on the scatter plot graph and the linear equation. (5 points)

Q2.5 Determine the predicted value of Y given X is 93.1. (2 points)

Q2.6 Plot the normal probability plot and the residual plot vs X. What do you infer from them? (5 points)

| X | Y |
|------|------|
| 78.4 | -9 |
| 89.9 | -18.2|
| 54.2 | -33.5|
| 58.3 | -25.6|
| 98.3 | -1.5 |
| 57.8 | -9 |
| 66 | -35.2|
| 67.1 | -20.3|
| 97.3 | -40.3|
| 76.5 | 0.3 |
| 86.1 | -16.1|
| 63.7 | 4.1 |
| 62.7 | -8.7 |
| 81.9 | -5.5 |
| 88 | -14.9|
| 60.9 | -19.8|
| 60.7 | 0.9 |
| 70.1 | -38.5|
| 86.7 | -5.8 |
| 94.4 | -33.7|
| 61.5 | -38.4|
| 72.4 | -26.2|
| 63.9 | -3.1 |
| 97.4 | -43.6|

Q2.1 To test the hypothesis that X is a good predictor of Y, we need to perform a regression analysis and examine the significance of the regression model. The regression model will help us determine if there is a statistically significant relationship between the independent variable (X) and the dependent variable (Y). We will perform a hypothesis test to evaluate the significance of the regression coefficients.

Q2.2 The parameters of the linear equation are as follows:

- Slope (β₁): The slope parameter represents the change in the dependent variable (Y) for a unit change in the independent variable (X). It indicates the rate of change in Y with respect to X.

- Intercept (β₀): The intercept parameter represents the value of the dependent variable (Y) when the independent variable (X) is zero. It determines the starting point of the linear relationship between X and Y.

Q2.3 To assess the strength of the model, we can use both the regression model and correlation analysis:

- Regression Model: The strength of the model can be evaluated by examining the coefficient of determination (R²). R² represents the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable (X). A higher R² value indicates a stronger relationship between X and Y.

- Correlation Analysis: We can calculate the correlation coefficient (r) between X and Y. The correlation coefficient measures the strength and direction of the linear relationship between X and Y. A value close to +1 or -1 indicates a strong linear relationship, while a value close to 0 suggests a weak relationship.

Q2.4 To show the linear line on the scatter plot graph and the linear equation, we'll plot the data points on a scatter plot and draw the best-fit line, which represents the linear equation. The linear equation can be expressed as Y = β₀ + β₁X, where β₀ is the intercept and β₁ is the slope.

Q2.5 To determine the predicted value of Y given X is 93.1, we substitute the value of X into the linear equation and calculate the corresponding Y value using the estimated slope and intercept from the regression analysis.

Q2.6 To plot the normal probability plot and the residual plot vs X, we'll analyze the normality of the residuals. The normal probability plot helps us assess whether the residuals follow a normal distribution. A straight line in the normal probability plot indicates that the residuals are normally distributed. The residual plot vs X helps us identify any patterns or deviations in the residuals, which may suggest issues with the regression model, such as heteroscedasticity or nonlinearity.

Note: To conduct a full regression analysis, including hypothesis testing, calculation of regression coefficients, and other statistical measures, we require statistical software or programming languages such as R or Python.

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