How to Calculate OLS Estimator with Given β0 in 50 Data Points?

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In summary, the OLS estimator for β1 can be derived by minimizing the dispersion function \sum {\left(Y_i - 3 - b_1 x_i\right)^2} using methods of one-variable calculus. The specific value can be found using the numerical information provided in the conversation. For more detailed steps, refer to the post provided.
  • #1
zmalone
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Homework Statement


ΣiYi = 500; ΣiXi = 150; ΣiYi2 = 17000; ΣiXi2 = 4000; ΣiXiYi = 8000; n = 50.

β0 = 3. Derive formula for OLS estimator of β1 and find estimate

Homework Equations


I'm new to OLS and I'm not sure where to go from:

Σ(Yi - 3 - b1Xi)^2

I was able to walk through the steps in my class lectures to solve Bhat1 and Bhat0 but am a little confused when β0 is given. Can anyone explain the logical following steps? Thank you!
 
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  • #2
Your dispersion function
[tex]
\sum {\left(Y_i - 3 - b_1 x_i\right)^2}
[/tex]

is now just a function of one unknown. Use methods of one-variable calculus to minimize it, then use the numerical information provided above to find the specific value
 
  • #3

1. What is the OLS estimator with given β0?

The OLS (Ordinary Least Squares) estimator with given β0 is a statistical method used to estimate the relationship between a dependent variable and one or more independent variables. It calculates the best-fitting line or curve by minimizing the sum of squared differences between the observed values and the predicted values.

2. How is the OLS estimator with given β0 calculated?

The OLS estimator with given β0 is calculated by finding the values of the slope and intercept that minimize the sum of squared differences between the observed values and the predicted values. This is done using mathematical equations and statistical software.

3. What is the purpose of using the OLS estimator with given β0?

The OLS estimator with given β0 is used to determine the strength and direction of the relationship between variables, and to make predictions based on this relationship. It is commonly used in regression analysis, where it can help identify the most important variables in a model and assess the significance of their effects.

4. What are the assumptions underlying the OLS estimator with given β0?

The OLS estimator with given β0 relies on several assumptions, including linearity (the relationship between variables is linear), independence of errors (the errors are not related to each other), homoscedasticity (the variance of errors is constant), and normality (the errors follow a normal distribution).

5. What are the advantages of using the OLS estimator with given β0?

The OLS estimator with given β0 is a simple and easy-to-understand method that can handle both continuous and categorical independent variables. It also provides unbiased estimates of the parameters and has a relatively low computational cost. Additionally, it allows for the use of statistical tests to assess the significance of the variables in the model.

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