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# Much has been written about the relationship between students’ SAT test scores and their family’s income. Generally speaking, there

Much has been written about the relationship between students’ SAT test scores and their family’s income. Generally speaking, there is a strong positive correlation between income and SAT scores. Consider and discuss the following questions as you respond:

What does this correlation tell you?
Is this correlation evidence that having a high family income causes one to have high SAT scores?
Is this correlation evidence that high SAT scores cause higher income? Or does this tell you something else? Explain your answer.
Explain why correlation alone is rarely sufficient to demonstrate cause.
Provide a personal example of two variables that may be correlated but not have a cause and effect relationship. Identify what type of bivariate correlation is involved, based on the measurement scales of the variables

## Time Series Statistics Questions

For statistical inference purposes you can use an?(significance) level of 0.05.For
each case, please clearly state your hypotheses, rejection criteria, and conclusionwhen needed.1. Consider a random walk model with no drift as follows?? =???1 ??where ?(??)=0,?(??)=?2 and ??? are uncorrelated.Show how you can obtain the autocorrelation function at lag k, denoted by ?? (Recallthat we have obtained the autocovariance function for a random walk in-class).2. Consider an AR model of order 2 as follows?? =?1???1 ?2???2 ??where ?(??)=0,?(??)=?2 and ??? are uncorrelated.- Show how you can obtain ?(??)- Show how you can obtain the autocovariance and autocorrelation functions at lagk as a function of ?1, ?2 autocovariances, and autocorrelations at lags k-1 and k-2. (Hint: you can take the above AR(2) equation and multiply both sides by ????and take the expectation to obtain ?(??,????)).3. Write a simulation sampler for a first order AR process for ?1 =0.5 (similar to ourrandom walk sampler from Set 3, rwsim.R). Please use a seed of 1 for your sampler.Obtain the time series, acf and pacf plots of the simulated series. Estimate an AR(1)model using the simulated series and investigate if the residuals are white noise.4. Consider the monthly price of gas in the US (Jan 1974-Dec 1982) given by gas.txt.a) Obtain the time series plot. Does this look like a stationary series?b) Obtain the ACF and the PACF of the series. Does this look like a random walk oran AR process?c) Obtain the ACF and the PACF of the first difference of the series. Does this looklike a random walk or an AR process?d) Estimate a random walk model and a suitable AR model on the differenced series.Test if the residuals are white noise for each case. Discuss the significance of the

model parameters for each model. Compare the AIC estimates. What do youobserve?e) Obtain a plot of the actual data versus your fitted random walk and AR modelsfrom part d.
Requirements: Math question | .doc file?

## HW statistic

Statistics Assignment Help There are 2 assignments:
1. In the Feeback file, please provide feedback to a student with a minimum of 80 words.
Please use vocabulary and techniques from the lecture to answer those questions.
Thank you

## A statistics’ homework. Don’t do question 7. The link for problem 1: https://www.economist.com/graphic-detail/2021/08/20/so-far-ending-pandemic-unemployment-aid-has-not-yielded-extra-jobs The link for problem 2: https://public.tableau.com/app/profile/klaus.schulte/viz/TotalAnnualLossofBeeColoniesintheUS/Dashboard1

A statistics’ homework. Don’t do question 7.

The link for problem 1: https://www.economist.com/graphic-detail/2021/08/20/so-far-ending-pandemic-unemployment-aid-has-not-yielded-extra-jobs

The link for problem 2: https://public.tableau.com/app/profile/klaus.schulte/viz/TotalAnnualLossofBeeColoniesintheUS/Dashboard1

The link for problem 3: https://computationalcommunication.org/ccr/article/view/86

The link for problem 4: https://www.social-searcher.com/

For question 5, I have attached the colab instructions pdf.

The link for question 6: https://math.typeit.org/

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