You are working on U$.$S$.$ stock market performances. You have been provided weekly adjusted close prices for the NASDAQ $($National Association of Securities Dealers Automated Quotations$)$ Composite index, Microsoft Corporation $($MSFT$),$ and Intel Corporation $($INTC$)$ from January $2014$ to December $2023.$

Please complete the following questions:

$1.$ Calculate weekly discrete returns for the NASDAQ index, Intel Corporation $($INTC$),$ and Microsoft Corporation $($MSFT$)$ stock prices, respectively. Please answer the following questions using the returns data obtained in Q$\mathrm{.}1.$

$2.$ Compute and interpret the descriptive statistics of NASDAQ index returns, Intel Corporation $($INTC$),$ and Microsoft Corporation $($MSFT$)$ stock prices returns, respectively.

$3.$ Which one has the highest relative risk among the weekly returns of the NASDAQ index, INTC and MSFT$?$ Provide evidence.

$4.$ Assuming normality, what is the probability of the INTC returns above $3\%?$ What is the probability of the MSFT returns being between $-2\%$ and $2\%?$

$5.$ Test whether the mean return of the NASDAQ index is significantly different from zero at the $1\%$ level of significance. Test whether the mean return of INTC is significantly different from $0\mathrm{.}5\%$ at the $5\%$ level of significance.

$6.$ What is the covariance of NASDAQ index returns and INTC returns? What is the correlation coefficient between the MSFT stock returns and INTC stock returns?

$7.$ To predict the weekly Intel Corporation $($INTC$)$ returns, your supervisor advised two linear regression models:

Model A: Assuming a linear relationship between INTC returns and MSFT returns.

Model B: Assuming a linear relationship between INTC returns and NASDAQ index returns.

$7\mathrm{.}1$: For model A$,$ is the intercept coefficient significant at the $5\%$ level? Is the slope coefficient significant at the $1\%$ level?

$7\mathrm{.}2$: For model B$,$ Construct the $99\%$ confidence interval for the intercept coefficient, and interpret it$.$

$7\mathrm{.}3$: Which model you would recommend to your supervisor, and why?