2. Consider fitting a model y = XB+ € where i~ id N(0,02). We have the following data: 1 0.7 1.2 X = 1 0.69 1.5 1 0.72 1.42 Y = (2.3, 1.8, 9.4) (a) Using the multivariate normal equations, calculate B = (B0, B1, B2). (b) Calculate the variance-covariance matrix of B. Based on your matrix, what is the variance of B1? What is the covariance of Bo and B1? (c) Suppose now that you care about the prediction for z given by: i. What is your best estimator for z? ii. What is the standard error for z? z = 0.880 +1.5231 Use python programming language to solve this question. Show steps by steps for me

A correlation of +.20 means that [blank] of the variance in the outcome variable is accounted for by the predictor variable.

The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? Use α=0.01. Weight, x 5920 5370 6500 5100 5890 4800 Variability in 1.76 1.91 1.50 braking distance, y EEE Click here to view a table of critical values for Student's t-distribution. Setup the hypothesis for the test. Ho: P Ha: P 0 0 1.86 1.62 1.67 M

The weight of cereal boxes (y) follows a normal distributed with a variance of 0.1 squared ounces. If the average is 15.8 ounces, then P(y < 16) = If the average is 16.5 ounces, then P(y > 16.2)

Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the...

A manufacturing company produces bearings. One line of bearings is specified to be 1.64 centimeters (cm) in diameter. A major customer requires that the variance of the bearings be no more than .001 cm2. The producer is required to test the bearings before they are shipped, and so the diameters of 16 bearings are measured with a precise instrument, resulting in the following values. Assume bearing diameters are normally distributed. Use the data and a = 0.01 to test to determine whether the population of these bearings is to be rejected because of too high a variance. 1.68 1.62 1.63 1.70 1.66 1.63 1.65 1.71 1.64 1.69 1.57 1.64 1.59 1.66 1.63 1.65 Appendix A Statistical Tables (Round your answer to 2 decimal places, e.g. 15.25.) The value of the test statistic is and we reject the null hypothesis ⇒

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H2. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd>d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169...