a) Construct a linear regression model
y = β0 + β1x ,
where y - stock price, x - time in minutes from 9am using the data in the Excel file StockPrices_HighFreq (under Files/Data sets).
Find the estimators of the coefficients of the model using the OLS approach (without using the Data Analysis Tool Pack). State the obtained model with the found estimated parameters. Find the 99% confidence intervals for each parameter of the model using the Data Analysis Tool Pack.
b) State the extrapolated price for the stock at 12:25pm (since the date is out of the range, this predicted value will be an extrapolation).
c) Show the scatter plot along with the regression line and its equation.
d) Find the residuals. Verify that their sum equals to 0. Verify that the sum of the products of the ith residual and the ith regressor equals to 0.
e) Interpret the meaning of the parameters β0 and β1 of the model (think what a slope and a y-intercept represent).
f) Test if the independent variable is significant in the model at significance level 99%. Specify the highest level of confidence at which one can claim that the independent variable is significant. Explain.
g) Calculate SST, SSE, SSR without using Excel Data Analysis Tool Pack Regression but compare your results with the output provided by the Excel Data Analysis Tool Pack Regression.
h) Find the coefficient of determination without using Excel Data Analysis Tool Pack Regression but compare your results with the output provided by the Excel Data Analysis Tool Pack Regression. Interpret the meaning of the coefficient.