Questions: 1-5

Q1.

Suppose you fit the first-order multiple regression model Y = B₀ + B₁X₁ + B₂X₂ + e to n = 25 data points and obtain the prediction equation Y = 50.11 + 5.44X₁ + 1.33X₂. The estimated standard deviations of the sampling distributions of B₁ and B₂ are 0.98 and 0.25, respectively.

a.  Test H₀: B₂ = 0 against H_a: B₂ > 0. Use Alpha = 0.10. to find this out determine test statistic and P-value

b.   Find a 99% confidence interval for B₂.

Suppose a statistician built a multiple regression model for predicting the total number of runs scored by a baseball team during a season. Using data for n = 200 samples, the results below were obtained. Complete parts a through d. (See the attached Table)

a.  Write the least squares prediction equation for y = total number of runs scored by a team in a season.

b.  Interpret, practically, B_o and B₁, in the model. Which statement below best interprets B_o?

c.  Conduct a test of H_o: B₅ = 0 against H_a: B₅>0 at α = 0.05. The test statistic is The p-value is the null hypothesis.

d.  Form a 90% confidence interval for B₄. Interpret the results.

Q2.

Researchers developed a safety performance function​ (SPF), which estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments of​ roadway, they fit the model E(y)=β₀+β₁x₁+β₂x₂​, where y=number of crashes per three​ years, x₁=roadway length​ (miles), and x2=average annual daily traffic​ (number of​ vehicles) equals=AADT.

a.  Give the least squares prediction equation for the interstate highway model.

b.  Give practical interpretations of the β estimates you made in part a. Interpret the value of β0. Choose the correct answer below.

c.  Refer to part a. Find a 99% confidence interval for β1.

d.  Refer to part a. Find a 99% confidence interval for β2.

e.  Give the least squares prediction equation for the interstate​ non-highway model.   

Q3.    Q4.    Q5.   included in the file.