Given the values: n= 20, xbar= 5, O y_hat = 3 + 2.4x O y_hat = 52 + 25x O y = Bo + B1x+ ɛ O y_hat = 12.4 + 36x %3D
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- Given the points (1, 1), (2, 3), (−3, 1), find the least squares regression line means of matrix operations.Percentages of public school students in fourth and eighth grades who were above the proficiency level were given for 8 western states 4th Grade Proficiency 8th Grade Proficiency Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 Construct a scatterplot and comment on any interesting characteristics Find the least squares equation. If Nevada had a 4th grade proficiency of 14%, what would you expect the 8th grade proficiency to be?Various doses of a poisonous substance were givento groups of 25 mice and the following results wereobserved: Dose (mg) Number of deathsx y4 16 38 610 812 1414 1616 20 (a) Find the equation of the least squares line fit tothese data.(b) Estimate the number of deaths in a group of 25 micethat receive a 7-milligram dose of this poison.
- How many indicator variables would be included in the model in order to prevent the least squares estimation from failing?In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.Researchers asked each child in a sample of 411 school-age children if they were more or less likely to purchase a lottery ticket at a store if lottery tickets were visible on the counter. The percentage that said that they were more likely to purchase a ticket by grade level are as follows: Grade Percentage that said theywere more likely to purchase 6 32.4 8 46.8 10 74.7 12 83.5 Find the equation of the least-squares line, where y = percentage who said they were more likely to purchase and x = grade. (Give the answer to two decimal places.) =
- What can you say from the models given? Maybe about the multicollinearity.Consider the data points (1, 0), (2, 1), and (3, 5). Compute the least squares error for the given line. In each case, plot the points and the line. y = -2 + 2x3.4 The system is tested on a sample of one hundred computers and the average connection speed is found to be far below 400 kilobits. What hypothesis should probably be rejected? Explain. If the customer needs a connection speed of 400 kilobits to run her application programs, what is the business decision that corresponds to the decision regarding the hypotheses?
- Explain the Formula for the Two Stage Least Squares estimator?A chemical company, seeking to study the effect of extraction time on the efficiency of an extraction operation, obtained the data from a table: Fit a straight line to the data given with the least squares method and use it to predict the extraction efficiency that would be expected when the extraction time is 35 minutes. x = Extraction time (minutes)y = Extraction efficiency (%)