Show explicitly that the following identity holds under a Simple Linear Regression: sum_(i=1)^n r_i mu_i=0 with residuals r_i=y_i-mu_i and mu_i=beta_0+beta_1 x_i

Read carefully and choose only one option 
A statistic is an unbiased estimator of a parameter when (a) the statistic is calculated from a random sample. (b) in a single sample, the value of the statistic is equal to the value of the parameter. (c) in many samples, the values of the statistic are very close to the value of the parameter. (d) in many samples, the values of the statistic are centered at the value of the parameter. (e) in many samples, the distribution of the statistic has a shape that is approximately Normal

Construct all random samples consisting three observations from the given data. Arrange the observations in ascending order without replacement and repetition.
86 89 92 95 98.

Find the mean of the following data: 12,10,15,10,16,12,10,15,15,13.

The equation has a positive slope and a negativey-intercept.
1) y=−2x−3
2) y=2−3x
3) y=2+3x
4) y=−2+3x

What term refers to the standard deviation of the sampling distribution?

Fill in the blanks to make the statement true: $30\%of₹360=\_\_\_\_\_\_\_\_$.

What percent of $240$ is $30$$?$

The first 15 digits of pi are as follows: 3.14159265358979
The frequency distribution table for the digits is as follows:
$\begin{array}{|cc|}\hline DIGIT& FREQUENCY\\ 1& 2\\ 2& 1\\ 3& 2\\ 4& 1\\ 5& 3\\ 6& 1\\ 7& 1\\ 8& 1\\ 9& 3\\ \hline\end{array}$
Which two digits appear for 3 times each?
A) 1, 7
B) 2, 6
C) 5, 9<br<D) 3, 8

How to write ${\displaystyle \frac{2}{20}}$ as a percent?

What is the simple interest of a loan for $1000 with 5 percent interest after 3 years?

What number is 12% of 45?

The probability that an automobile being filled with gasoline also needs an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.10. (a) If the oil has to be changed, what is the probability that a new oil filter is needed? (b) If a new oil filter is needed, what is the probability that the oil has to be changed?

Leasing a car. The price of the car is​$45,000. You have ​$3000 for a down payment. The term of the lease is and the interest rate is ​3.5% APR. The buyout on the lease is​51% of its purchase price and it is due at the end of the term. What are the monthly lease payments​ (before tax)?

The mean of sample A is significantly different than the mean of sample B. Sample A: $59,33,74,62,87,73$ Sample B: $53,67,72,57,93,79$ Use a two-tailed $t$-test of independent samples for the above hypothesis and data. What is the $p$-value?

What is mean and its advantages?