6. One of your fellow Clark students wrote an honors thesis this year trying to understand...

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6. One of your fellow Clark students wrote an honors thesis this year trying to understand the effects of Covid-19 on mental health. She used several years of a large nationally representative quarterly data to run a regression model of a depression score on Covid-19 death rates and vaccine rates. She found the following output below. Use 95% confidence level to answer this question. Model 1: Dependent variable: Mental distress score Coef Death Rate 0.000706 p-value 0.019 Lower Bound of Confidence Interval Upper Bound of Confidence Interval Vaccine Rate Constant -0.0029 -0.00445 -0.00135 1.542 0.003 a) Is the Covid-19 death rate a statistically significant predictor of mental distress? Explain. 2 points b) Is the Covid-19 vaccine rate a statistically significant predictor of mental distress? Explain. 2 points c) The student hypothesized that one reason Covid-19 affected people's mental health was because of the economic impact of the pandemic. She regressed (log) income on death rate and vaccine rate to test this hypothesis (output below). What did she find? Was Covid-19 death rate statistically significantly associated with lower income? 2 points Model 2: Dependent variable: log of income Death Rate Coef -0.0000617 STE 0.000072 Vaccine Rate Constant 0.000244 0.00018 2.300 0.009 6. One of your fellow Clark students wrote an honors thesis this year trying to understand the effects of Covid-19 on mental health. She used several years of a large nationally representative quarterly data to run a regression model of a depression score on Covid-19 death rates and vaccine rates. She found the following output below. Use 95% confidence level to answer this question. Model 1: Dependent variable: Mental distress score Coef Death Rate 0.000706 p-value 0.019 Lower Bound of Confidence Interval Upper Bound of Confidence Interval Vaccine Rate Constant -0.0029 -0.00445 -0.00135 1.542 0.003 a) Is the Covid-19 death rate a statistically significant predictor of mental distress? Explain. 2 points b) Is the Covid-19 vaccine rate a statistically significant predictor of mental distress? Explain. 2 points c) The student hypothesized that one reason Covid-19 affected people's mental health was because of the economic impact of the pandemic. She regressed (log) income on death rate and vaccine rate to test this hypothesis (output below). What did she find? Was Covid-19 death rate statistically significantly associated with lower income? 2 points Model 2: Dependent variable: log of income Death Rate Coef -0.0000617 STE 0.000072 Vaccine Rate Constant 0.000244 0.00018 2.300 0.009