Show that E(y^2)= standard deviation square y plus residual square capital Y
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- A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.778b=0.143 (d) If the life expectancy is increased by 5 years in a certain country, how much will the happiness index change? Round to two decimal places.(e) Use the regression line to predict the happiness index of a country with a life expectancy of 94 years. Round to two decimal places.A researcher collects data between the age in years, (x), of a movie theater's popcorn popper and the cost of its monthly maintenance,(y).Find the regression equation. Round b to three decimal places.ˆyy^ = + CorrectxxFill in the table to find the residuals. Round table entries to three decimal places. xx yy ˆyy^ y−ˆyy-y^ 8 58 9 98 15 102 4 32 7 60 3 31 2 25 What is the correlation coefficient? Round to three decimal places. Graph the data and find the outlier. Give the ordered pair here:(, )If your ordered pair is actually the outlier, then the correlation coefficient would increase. Delete the ordered pair you chose and find the correlation coefficient again. Type the new correlation coefficient rounded to three decimal places here: Put the outlier back into your data and then find the test statistic, p-value, df, and critical value(s) for a test to find if there is a positive correlation with α=0.01α=0.01. Round to 3 decimal placestt…For the linear regression model Y = bo + b1(X): The p-value for the intercept is large: about 0.98 The p-value for the slope is very small: less than 2 times 10^(-16) What can we conclude? Since the p-value for the intercept is large, we can conclude that there is not a strong correlation between X and Y. Since the p-value for the intercept is large, we can conclude that there is a very strong correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very weak correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very strong correlation between X and Y. We are not able to assess the strength of the correlation between X and Y with the output provided.
- The table below represents the values of discharge and stage. Extend the rating curve for these data, using the following equations [q= k(g-a), k= 10^, a=0]. Try to estimate the values of k and b by least square method. Determine the value of discharge at stage 7m. Stage (m) 5. 4 2 Discharge (m'/s) 50 20 108. In a regression model if you drop one insignificant variable then A. R ^ 2 will decrease but SSE will increase. B. R ^ 2 will increase but SSE will decrease. C. R ^ 2 will increase and SSE also will increase. D. R ^ 2 will decrease and SSE also will decrease. E. NoneA study of king penguins looked for a relationship between how deep the penguins dive in meters (x) and how long they stay underwater in minutes (y). The study reported that the regression equation was ˆy=−0.044x+4.937y^=-0.044x+4.937 and the coefficient of determination was 0.81What is the correlation coefficient for this data set (round your answer to 2 decimal places)?
- 26) Below is some of the regression output from a simple regression of the number of wins for a major league baseball team and the size amount of money the team is paying its players (expressed in millions of $'s) *fill in the blank table* Suppose that the team owner is trying to decide whether to pay a particular free agent player. Based on the player's previous statistics, the owner thinks that the new player can help his team increase the number of wins but the new player is going to cost more than the player he will be replacing. The owner decides it is a good idea to sign the new player if he can be pretty sure that the coefficient is at least 0.20. When testing this hypothesis, what is the test statistic? (please express your answer using 2 decimal places)when using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?Suppose you obtain the following regression model, E[y]=20+53*x +33*x^2. What is the impact of a 63 unit change of x on the expected value of y when x is at its mean of 54?
- Distinguish Experimental Conditions from Experimental Unit.Suppose you obtain the following regression model, E[y]=20+47*x +88*x^2. What is the impact of a 64 unit change of x on the expected value of y when x is at its mean of 57?The standard error estimate is computed as the square root of the mean squared error and it is a standard deviation of the errors. It is therefore useful for to making a judgment about the fit of regression model in conjunction with the assumption that the model is linear the error terms are normally distributed the error terms are independent the error terms have constant variance