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If an automobile is driven on the average no more than 16000 Km per year, then formulate the null and alternative hypothesis.
. f (x, y,z) = k exp [− 1/2 (2x2 − 2xy + y2 + z2 + 2x − 6y) .
1. Compute k.
2. Compute the expectations P(X), P(Y ) and P(Z).
3. Compute the density of the random vector (X, Z).
4. Compute the correlation coeffificient between X and Z and between X and Y .
5. Let W = X + Z; compute the probability density of W.
f (x, y) = K x for y ≤ x ≤ y + 1, 0 ≤ y ≤ 2,
= 0 otherwise.
(a) Compute K.
(b) Compute the m.d.f. and the expectation of X.
by chance 3 pupils, one out of each school, at least one of them wears glasses, is
to evaluate the probability that none of them wears glasses. If B is the event that
at least one of the 3 pupils wears glasses.
1. Use the data file wage to work on using STATA and answer the following questions
a) Examine the data
b) Carry out remedial measure(s) if there is any problem with data
c) Regress HRS on RATE, ERSP, ERNO, NEIN, AGE and DEP
d) Conduct model specification tests using linktest and ovtest commands of STATA, and interpret the result
e) Perform multicollinearity test
f) Perform hetroscedasticity test
g) Comment on the explanatory power and adequacy of the model
h) Interpret the regression coefficients
1. Discuss the nature, causes, consequences and remedies of each of the following problems we might encounter in regression analysis.
a) Muticollinearity
b) Hetroscedasticity
c) Autocorrelation
1. The following data refers to the price of a good ‘P’ and the quantity of the good supplied, ‘S’.
p 2 7 5 1 4 8 2 8
___/_____________________________________
s / 15 41 32 9 24 43 17 40
a. Estimate the linear regression line
b. Estimate the standard errors of
c. Test the hypothesis that price influences supply
A random sample of high school students are asked the number of hours they spent on social media. The hours are reported below:
3
5
6
7
8
10
12
13
14
15
You can assume the times are normally distributed with a standard deviation of 8.5.
a) Estimate with 90 percent confidence the mean number of hours spent on social media by all high school students. Show all working as part of your answer.
b) Interpret your findings in part a).
#339914 on Dec 2023