Given the information below calculated from data collected from a sample of 8 students relating study time (x in hours per week) and leisure time (y hours per week) find the equation of the regression line relating y to x. X 59.37 Y = 4.25 SS= 1843.S7 SS = -49.75 SS, = 7.5 %3! O Y-hat = +0.027x + 59.37 O Y-hat = - 0.027x + 59.37. O Y-hat = + 4,25x + 59.37 Y-hat - 0.027x + 5.85 Y-hat 0.027x + 5.85
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- Use the table of values you made in part 4 of the example to find the limiting value of the average rate of change in velocity.The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.In a certain dynamic measurement application the input(x) – output(y) relationship is given by y=1+(1+x)e-x With what uncertainty must x be determined to yield a relative uncertainty of ±2 percent for y at a value of x = 3,8?
- The data given below indicate the existence of a linear relationship between the x and y variables. Suppose an analyst who prepared the solutions and carried out the RI measurements was not skilled and as a result of poor technique, allowed intermediate errors to appear. The results are the following:Concentration of solution in percent (x) 10 26 33 50 61Refractive indices (y) 1.497 1.493 1.485 1.478 1.477Step 1. Carefully plot the given x and y values (from the table) on a regular graphing paper. Label then connect the points to observe a zigzag plot due to the scattered points. Step 2: Copy and fill the table given below: x (x - x̄) (x - x̄) 2 y (y - ȳ) (y - ȳ) 2 (x - x̄) (y - ȳ) 10 1.497 26 1.49333 1.48550 1.47861 1.477∑ = ∑ = ∑ = ∑ = ∑ = ∑ = ∑ =x̄= ∑xi ÷ Nx̄= ȳ = ∑yi ÷ Nȳ = Step 3. After completing the table, present following computations and the interpretation.a. Calculate the correlation coefficient (r), using the working formula: r =Σ (x − x ) (y − ȳ)√(Σ(x − x )2)(Σ(y −…We showed that in a simple linear regression, the MLE estimates for ?1 and ?0 are the same as the OLS estimates. Show that the MLE estimate (Hint: take the derivative of the LL w.r.t ?2).28. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation is:Price = 1,251 + 0.34*Size + 1,538*View + 0.07*(Size*View) Suppose you just built a house with an ocean front view that is 3600 square feet and you want to decide how much to rent it for. What is the predicted price of a house that is 3600 square feet and has an ocean front view? (please express your answer using 1 decimal places)
- For the situation described below, state the null and alternative hypotheses to be tested. (Enter != for ≠ as needed.) A seed wash is expected to change the proportion p of seeds that germinate when planted in poorly-draining soil. Suppose that the current germination rate is about 70%.You give a final attempt to bring the effect of Size back into the equation by forcing the assumption of homoskedasticity onto your estimation. The results are as follows: cost^= = 7,311.17 + 3,985.20 × Reputation – 0.20 × Size (1,985.17) (593.65) (0.07)+ 8,406.79 × Dpriv – 416.38 × Dlibart – 2,376.51 × Dreligion (1,423.59) (1,096.49) (989.23) R 2=0.72, SER = 3,682.02Calculate the t-statistic on the Size coefficient and perform the hypothesis test that its coefficient is zero. Is this test reliable? Explain.he following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The multiple coefficient of determination is
- A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 7; Mx = 3 What is b equal to (Please include the sign: e.g., -20)? What is a equal to (please include the sign: e.g., +4.0)? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?For the production function Q (K,L)= 1000 (KL3 )1/3 , Given the current input level K = 400 and L = 40. Use marginal analysis to estimate the approximate change in output which results form an increase in K of 9 units and a decrease in L of 7 units. Verify that Young′s Theorem holds?At Chairs and More, assemblers are paid according to the following differential piece rate of scale 1-25 chairs in a week, $10 each ; 26-40 chairs in a week $13 each;