A statistical program is recommended.

Spring is a peak time for selling houses. Suppose the data below contains the selling price, number of bathrooms, square footage, and number of bedrooms of 26 homes sold in Ft. Thomas, Kentucky, in spring 2018.

Consider the estimated regression equation we developed that can be used to predict the selling price given the number of bathrooms, square footage, and number of bedrooms in the house.

(x₁ denotes number of bathrooms, x₂ denotes square footage, x₃ denotes number of bedrooms, and y denotes the selling price.)

ŷ = −1770.46 + 18130.69x₁ + 60.00x₂ + 40706.14x₃

(a)

Does the estimated regression equation provide a good fit to the data? Explain. (Round your answer to two decimal places.)

Since the adjusted R²= _____

(b)

Consider the estimated regression equation that was developed which predicts selling price given the square footage and number of bedrooms.

(x₂ denotes square footage,  x₃ denotes number of bedrooms, and y denotes the selling price.)

ŷ = 7679.47 + 67.88x₂ + 44959.40x₃

Compare the fit for this simpler model to that of the model that also includes number of bathrooms as an independent variable. (Round your answer to Three decimal places.)

The adjusted R² for the simpler model is:_____

two balls, ball 1 and ball 2are about collide heads on a frictionless linear track. Ball 1 is traveling east with a speed 8m/s toward ball 2. Ball 2 has a speed of 4 m/s. If the mass of the ball 2 is 8 times the mass of ball 1 what is the speed of ball 2 after the collision? We asume that the collision id perfectly elastic

A psychologist would like to examine how the rate of presentation affects people’s ability to memorize a list of words. A list of 20 words is prepared. For one group of participants the list is presented at the rate of one word every ½ second. The next group gets one word every second. The third group has one word every 2 seconds, and the fourth group has one word every 3 seconds. After the list is presented, the psychologist asks each person to recall the entire list. The dependent variable is the number of errors in recall. The data from this experiment are as follows:

Step by step on SPSS

a. Can the psychologist conclude that the rate of presentation has a significant effect on memory? Test at the .05 level.

b. Use the Tukey HSD test to determine which rates of presentation are statistically different and which are not.

Probability theory and the binomial expansion show that, were you to sample families consisting of four children 1/16 of these families would consist of 4 boys, 4/16 would consist of 3 boys and 1 girl, 6/16 would consist of 2 boys and 2 girls, 4/16 would consist of 1 boy and 3 girls, and 1/16 would consist of 4 girls. Do the data in the sample given in the next table approximate this expectation? Complete the table, calculate X², and answer the questions based on your calculations.

A. interpret this X² value, you have __________ degrees of freedom.

b. In this case do you accept/reject the hypothesis that these data approximate a dihybrid test cross ratio with independent assortment?a. In interpreting this X² value, you have _____ dregrees of freedom.

c. What is the probability that the deviations are due to chance alone?

D. Determine whether the overall ratio of boys to girls in the above data is consistent with the hypothesis of a 50:50 sex ratio. Remember that each family included in the table consists of four children; for example, 235 families consisted of 4 boys, 898 families consisted of 3 boys and 1 girl, and 1317 families consisted of 2 boys and 2 girls. Calculate X² for these data by completing the following table:

E. Accept/Reject ________; df=_____________; P=___________

F. Calculate the ratio of boys to girls; record here:

G. How have biologists explained sex ratio data such as those observed in this problem?

Please explain the steps...... Thanks

Let the random variable X and Y have the joint pmf f(x, y) = , c xy 2 where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are {(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} .

(a) Find c > 0 .

(b) Find μ . X

(c) Find μ . Y

(d) Find σ . 2 X

(e) Find σ . 2 Y

(f) Find Cov (X, Y ) .

(g) Find ρ , Corr (X, Y ) .

(h) Are X and Y independent?

Please show work/explanation if you can, thank you!

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $253,000 and will yield the following expected cash flows. Management requires investments to have a payback period of 3 years, and it requires a 7% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the table provided.)

Required:
1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

Determine the payback period for this investment. (Enter cash outflows with a minus sign. Round your Payback Period answer to 1 decimal place.)

Determine the break-even time for this investment. (Enter cash outflows with a minus sign. Round your break-even time answer to 1 decimal place.)

Determine the net present value for this investment.

The owner of a large equipment rental company wants to estimate the average number of days a piece of equipment is rented out. A random sample of 14 rental invoices reveals the following number of days;

3       1       3       2       5       1       2       1     4       2       1       3       1       1

a. Determine the sample mean.

b. Determine the sample standard deviation.

c. Using the 99% level of confidence, determine the confidence interval for the population mean.

A research paper describes an experiment in which 74 men were assigned at random to one of four treatments.

1. viewed slides of fit, muscular men
2. viewed slides of fit, muscular men accompanied by diet and fitness-related text
3. viewed slides of fit, muscular men accompanied by text not related to diet and fitness
4. did not view any slides

The participants then went to a room to complete a questionnaire. In this room, bowls of pretzels were set out on the tables. A research assistant noted how many pretzels were consumed by each participant while completing the questionnaire. Data consistent with summary quantities given in the paper are given in the accompanying table.

Do these data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments? Test the relevant hypotheses using a significance level of 0.05.

Calculate the test statistic. (Round your answer to two decimal places.)

F =

What can be said about the P-value for this test?

P-value > 0.1000.050 < P-value < 0.100    0.010 < P-value < 0.0500.001 < P-value < 0.010P-value < 0.001

What can you conclude?

Reject H₀. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.Fail to reject H₀. The data do not provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.    Reject H₀. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.Fail to reject H₀. The data provide convincing evidence that the mean number of pretzels consumed is not the same for all four treatments.

You may need to use the appropriate table in Appendix A to answer this question.

Calculate the elasticity for the following questions (USING THE MIDPOINT (AVERAGE) FORMULA) and indicate if the goods are:

1. Inferior,
2. Normal,
3. Complements, or
4. Substitutes

(Please Include The Negative signs in your answers where appropriate)

A. The price of gasoline increases from 12 per barrel to 28 per barrel and as a result, the demand per month for new cars changes from 600 to 200.

Part 1: The elasticity is


Part 2: These goods are (answer using numbers, 1-4)

B. As a result of a change in income from 1,275 to 1,875 per month, the consumption of good X changes from 380 to 200 units.


Part 3: The elasticity is



Part 4: Good X is a(an) (answer using numbers, 1-4)


C. As a result of a decrease in the price of good Y from 39 to 19 the demand for good X changes from 150 to 350 units.


Part 5: The elasticity is



Part 6: These goods are(answer using numbers, 1-4)


D. As a result of an economic boom in Calgary, the average income increases from 2,800 to 4,200 per month and as a result the demand for new houses increases from 160 to 260 units.


Part 7: The elasticity is



Part 8: New houses are a(an) (answer using numbers, 1-4)

Calculate the elasticity for the following questions (USING THE MIDPOINT (AVERAGE) FORMULA) and indicate if the goods are:

1. Inferior,
2. Normal,
3. Complements, or
4. Substitutes

(Please Include The Negative signs in your answers where appropriate)

A. The price of gasoline increases from 20 per barrel to 30 per barrel and as a result, the demand per month for new cars changes from 650 to 300.

Part 1: The elasticity is


Part 2: These goods are (answer using numbers, 1-4)

B. As a result of a change in income from 1,475 to 2,975 per month, the consumption of good X changes from 340 to 425 units.


Part 3: The elasticity is



Part 4: Good X is a(an) (answer using numbers, 1-4)


C. As a result of a decrease in the price of good Y from 31 to 20 the demand for good X changes from 300 to 350 units.


Part 5: The elasticity is



Part 6: These goods are(answer using numbers, 1-4)


D. As a result of an economic boom in Calgary, the average income increases from 2,500 to 5,500 per month and as a result the demand for new houses increases from 150 to 360 units.


Part 7: The elasticity is



Part 8: New houses are a(an) (answer using numbers, 1-4)