Question:

which of the following is a true statement for a regression analysis?

-regression analysis is applied only to a non-linear model

-regression analysis is applied only to a multiplicative model

-regression analysis is applied only to a linear model

-regression analysis is applied only to an exponential model

an experiment with more than one manipulated factor is called

-simple random design

-non-randomized block design

-factorial design

-none of the above

While regression analysis is a useful tool for making budgeting predictions, learning how to become proficient in regression analysis is beyond the scope. But, knowing what regression analysis can do for the budgeting process is important. Write a short paragraph, or two, explaining what you feel regression analysis can provide during the budgeting process.

In Hypothesis Testing the "Null Hypothesis", Ho, assumes and means:

All observed results in regression analysis are the result of systemic causes;

All observed results in the regression analysis are the result of random chance;

Has nothing to do with regression analysis;

None of the above.

19.In Hypothesis testing the "Alternative Hypothesis", H(A), assumes and means:

All observed results in regression analysis are the results of random chance;

Observed results in the regression analysis are the results of systemic causes with random change having limited probability of effecting the results;

Has nothing to do with regression analysis;

All of the above;

While regression analysis is a useful tool for making budgeting predictions, lear

Fit a power-law equation of the form y = ax" to the following set of experimental data using least-squares fitting techniques. Report the values of a, b, and the correlation coefficient r. (i) Plot the raw data points and the least-squares fit on linear graph paper and (ii) Plot the raw data points on log-log paper (or plot In y vs. In x on linear paper). Note: Do not perform these plots on excel spreadsheets. Plot these manually on actual graph paper. You can download these in Coursesite. X y 0.5 1.96 1.0 2.54 1.5 2.77 2.0 3.23 2.5 3.34 3.0 3.66 3.5 3.763. Using Microsoft Excel , plot the sample data contained in Table 1 Table 1. in an XY (Scatter) plot. Right Click on a data point on the chart and X y select Add Trendline. Be certain Linear is highlighted in the Type tab 1.4 217 2.6 185 and in the Options tab click the boxes to display the equation and R- 4.1 126 squared value on the chart. Excel uses the method of least-squares 5.7 97 fitting to obtain the line. Submit the chart with equation and R-squared 6.8 91 value clearly displayed. 8.9 53 10.2 11 - 1 -We want to perform a least squares fitting of a quadratic function y = atz + ait + do (3) to a given data set {(t1, y1), (t2, y2), (t3, 43), (t4, y4), (t5, 95) }. (4) 1. Construct the corresponding Vandermonde matrix V. 2. Write a linear system that gives the best values of a2, a1, and do. 3. Suppose you define the following two vectors in MATLAB: tvec=[t1 t2 ta ta t5]' yvec=[y1 92 y3 y4 y5]' How would you define the Vandermonde matrix V and compute the vector avec=[a2 a, a]' of the least squares fitting in MATLAB?Choose one FALSE statement about a correlation coefficient in a linear regression analysis. A correlation coefficient is never greater than 1 or less than -1. A correlation coefficient is always less than the coefficient of determination (r?). A correlation coefficient of -0.9 shows a stronger correlation between the variables than a correlation coefficient of 0.8. O A correlation coefficient of 0 means there is no correlation at all between the variables. A correlation coefficient always has the same sign as the slope of a linear regression equation. Submit QuestionConsider the 3 points of data (t1, b1) = (0, 6), (t2, b2) = (1,0), (ta, b3) = (2, 0) which we want to fit to a parabola b = C + Dt + Et2 using the least squares approximation. 1. (20) Write the Ax = b system of equations we would like to solve and clearly identify A, x and b. 2. (20) What is the projection matrix P corresponding to this least squares fitting? You do not need to present any calculations but you need to fully justify your answer. e = 3. (20) What is the error vector corresponding to this least squares fitting? Justify. 4. (20) List all the vectors orthogonal to this error vector. Justify. 5. (20) Suppose there was a reformulation and the problem now is to find the best solution to Find P, the projection matrix, and p, the projection, in this case. Justify