Fit the data in the following table to the exponential model, y = C₁ et using Find c₁ and c₂ to the fourth place after the decimal point. linearization. t y -2 4 -1 2 1 1 2 1/2

Consider fitting a linear regression he(x) = 0Tx = 01x1+ 02x2+ O3x3 to a training dataset D = {(x1,y1),..., (xn, Yn)}, where 0 = [01, 02, 03]T and x = [#1, x2, 83]T Q1.1 Let D = {([1,0, 0]",0), ([0, 1, 0]" , 0.5), ([0, 0, 1]", – 1)}. Our current estimate of the parameter 0 = [0, 0, 0]T. which training instance makes the smallest contribution to the gradient ? (contribution means the magnitude of gradient change) O 1 O 2 O 3 Q1.2. What is the updated parameter after one step of gradient descent (assuming step size = 1)? O [0, 0, 0]T O (0, 1, 0]" О (), 0.5, — 1]7 O [0, 0.5, 1]"

In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…

The value y (in 1982-1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.676) (1996, 0.638) (1998, 0.608) (2000, 0.584) (2002, 0.556) (2004, 0.528) (2006, 0.494) (2008, 0.461) (1995, 0.658) (1997, 0.622) (1999, 0.599) (2001, 0.568) (2003, 0.543) (2005, 0.509) (2007, 0.486) (a) Use a spreadsheet software program to generate a scatter plot of the data. Let t = 4 represent 1994. Do the data appear linear? O Yes No (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let t represent time. Round your numerical values to four decimal places.) y 3= (c) Use the model to predict the value (in 1982-1984 dollars) of 1 dollar paid by consumers in 2010 and in 2013. (Round your answers to two decimal places.) 2010 2013 24 Discuss the reliability of your predictions based on your scatter plot and the graph of your linear model for the data. Because the…