Search & Filtering
Suppose you have a Simple population regression function describe as follows derive the ordinary least squares estimator of the coefficients.
during a high school spirit week student dress up in costumes. a cash price is given to students with the best costume the organization committee has $1000 to give away over 5 days the committee wants to increase the price by $50 each day how much should the committee give away on the first day?
You are a researcher who is interested in how watching television influences children’s performance in school. You find out how many hours of television 5 children watch, on average, in a week. You have obtained their overall grade average.
Child No. Hours of TV Overall Grade Average
1 5 80
2 20 67
3 6 75
4 14 70
5 12 80
a. Calculate the correlation between hours of television watched and overall grade average. Interpret the correlation – what does it mean?
b. Calculate the regression equation (use television watching to predict grade).
c. Make a scatter plot of the data and draw the line of best fit on your scatter plot.
A bowl contains 6 blue balls, 8 red balls, 6 white balls, and 10 yellow balls. What is the probability of picking a yellow ball?
Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of
compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the
treatments (cars types). Using the hypothetical data provided below, test whether the mean
pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.
Compact cars Midsize cars Full-size cars
643 469 484
655 427 456
702 525 402
Mean 666.67 473.67 447.33
Standard 31.18 49.17 41.68
deviation
In a market survey conducted to examine whether the choice of a brand is related to the income levels of the consumers, a random sample of 400 consumers reveal the following:
Income level Brand 1 Brand 2 Brand 3 Total
per month
20000 93 72 75 240
20000-50000 50 35 37 122
>50000 12 15 11 38
Total 155 122 123 400
Test the association between income level and brand preference at 5% significant level.
If f(x,y) = x^3 + 4xy^2 + y^3, show that f(ax, ay)= a^3 f(x,y).
If f(x) =10^x and Φ(x) =log10 x, show that f[Φ(x)] = Φ [f(x)] = x.
If f(x)= x^2 -1 and g (x) =2x +1, show that f[g(x)]=4x(x+1).
If f(x) = sin x, show that f (2x)= 2f(x) f(1/2 π-x).
