Two random variables X = (1,2) and Y= (-2,-1] are equiprobable and independent. Determine the correlation factor r(X,Y),
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- Consider a set of data (x₁, yi), i=1,2,..0 and the Simple linear regression equation given by : 4 y₁ = B₁+ B₁²x₁ The /s Standardized random variable of given by 2= B₂₁ - B²₁₂² FSSxx find the mean and the variance of ZoIf var(X) = var(Y) = σ², cov(X,Y)= and 2Y-3 find the correlation between 2X+3The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables number of years Espa spent by the student at the university and score on the first midterm have a sample correlation coefficient r of about -0.36. Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H . Aa 0, B H, :0 H : O=0 (b) Determine the type of test statistic to use. (Choose one) ▼ OA sample of 30 ordered pairs produces a linear correlation coefficient of r-0.026 Which of the following statements would be true? No regression line could be calculated from these ordered pairs Although no linear correlation exists, there might be a strong non-linear correlation A negative linear correlation exists A positive linear correlation exists The regression line would not pass through the point (x, y)Prove that coefficient of determination is square of correlation coefficientTrue or False: A semi-partial correlation will always be smaller than a zero-order correlation.Answer allWhat information is provided by r2? What are the primary uses of partial correlations?There are two random variables X and Y, and their correlation coefficient pX,Y = 0.7. Now, we have two new random variables A = 2.5X+1 and B = 4Y+2. Please compute the correlation coefficient of A and B, PA,B Please round your answer to one decimal place.Amount of brake fluid can affect the breaking time of a vehicle. Engineer Nsiah conducts an experiment to determine if this statement is true. The breaking time data for the trials for different levels of brake fluid as presented in table below. i) Obtain the linear regression model for the given data ii) Compute the correlation coefficient, r iii) Find the Breaking time given the amount of oil is 45cm2 Amount of 20 10 30 40 60 50 oil(cm3) Braking time(s) 9. (iv) The coefficient of determination, r for the given data 3.Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient. Please dont use excel.Calculate estimates of the standard deviations sz, Sy of the samples r = (5,9, 7) and y = (-1,2,5) as well as the Pearson coefficient of correlation rry of r and y. Which of the following answers are correct? a) sz = 4, sy = 9 b) rzy = 0 c) sz = 2, sy = 3 d) Tzy = } e) rzy =
