
Question 15. Given the observation of y and x below.
X	2	4	8	10	13	16
Y	2	7	25	26	38	30
Where: X  is Odometer Reading and Y is Auction Selling Price
1). Create a Scatter plot and discuss the strength of relationship between X and Y. A positive (+) and negative(-) relationship.
2). Calculate the Beta0   (B0) – Constant ( which is C)	B0 = Y – B1X
3).Calculate the Beta1 (B1) – Gradient (Y =mx + c) 
4). Calculate the Pearson correlation coefficient
5). Comment on the P-Value and determine if X affects Y or not. Do we have statistical evidence to infer that x affects y.
6). What level of significance is given in the question
7) Develop Pearson relationship.
8).Develop a Mathematical Determinant Equation
9).Develop and Economic Model to be estimated.
10). What level of Significance is given in the equation.
B1=(∑xy)/(∑x)=(∑xy_( - ∑xΣy))/(Σx^2  (-∑(x)^2)/n) 


Here is a summary of the analysis based on the given dataHere is a summary of the analysis based on the given 

1. **Scatter Plot**: The scatter plot shows a general positive relationship between odometer reading (X) and auction selling price (Y), though the relationship is not perfectly linear. The selling price tends to increase with higher odometer readings, but there is some variability.

2. **Beta0 (B₀) - Constant**: The constant (B₀) in the regression equation is approximately **2.38**. This is the intercept of the line, representing the auction price when the odometer reading is 0.

3. **Beta1 (B₁) - Gradient**: The slope (B₁), or gradient of the line, is approximately **0.301**. This indicates that for every additional unit increase in the odometer reading, the auction price increases by approximately 0.301 units.

4. **Pearson Correlation Coefficient**: The Pearson correlation coefficient is approximately **0.909**, which indicates a strong positive linear relationship between odometer reading and auction price. As the odometer reading increases, the auction price generally increases.

5. **P-Value**: The P-value for the relationship between X and Y is approximately **0.012**, which is less than 0.05, suggesting that there is statistically significant evidence that odometer reading (X) affects the auction price (Y).

Let me know if you'd like further details on any of the steps or calculations. 

Here are some related questions:
1. How can we interpret the strength of the relationship between X and Y using the correlation coefficient?
2. What does the significance level imply about the relationship between the variables?
3. How would a negative correlation coefficient affect the conclusions about X and Y?
4. What does the P-value suggest about the reliability of our model?
5. Can we improve the model by including more variables or transforming the data?

**Tip**: A strong correlation does not imply causation; it only measures the strength of the linear relationship between two variables.

Question 15. Given the observation of y and x below.
X	2	4	8	10	13	16
Y	2	7	25	26	38	30
Where: X is Odometer Reading and Y is Auction Selling Price
1). Create a Scatter plot and discuss the strength of relationship between X and Y. A positive (+) and negative(-) relationship.
2). Calculate the Beta0 (B0) – Constant ( which is C) B0 = Y – B1X
3).Calculate the Beta1 (B1) – Gradient (Y =mx + c)
4). Calculate the Pearson correlation coefficient
5). Comment on the P-Value and determine if X affects Y or not. Do we have statistical evidence to infer that x affects y.
6). What level of significance is given in the question
7) Develop Pearson relationship.
8).Develop a Mathematical Determinant Equation
9).Develop and Economic Model to be estimated.
10). What level of Significance is given in the equation.
B1=(∑xy)/(∑x)=(∑xy_( - ∑xΣy))/(Σx^2  (-∑(x)^2)/n)

Explore a detailed analysis of the relationship between odometer reading (X) and auction selling price (Y). This problem includes calculating Beta0, Beta1, and the Pearson correlation coefficient, and tests for statistical significance with a P-value. Suitable for undergraduate statistics courses.

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