Question

12.4 For each of the following, explain what is wrong and why. (a) (1m) A 95%...

12.4 For each of the following, explain what is wrong and why.

(a) (1m) A 95% confidence interval for the mean response is the same width regardless of the value of x.

(b) (1m) To test H0: b1 = 0, use a t test.

(c) (1m) For a particular value of the explanatory variable x, the confidence interval for the mean response will be wider than the prediction interval for a future observation

0 0
Add a comment Improve this question Transcribed image text
Answer #1

(a) (1m) A 95% confidence interval for the mean response is the same width regardless of the value of x.

In this statement the wrong part is that interval is same as width but it is not true, width changes with respect to value of x.

(b) (1m) To test H0: b1 = 0, use a t test.

Here in order to test the slope of regression we want to use a t-statistic

with (b1- hypothesized value) / SE(b1).

(c) (1m) For a particular value of the explanatory variable x, the confidence interval for the mean response will be wider than the prediction interval for a future observation.

The prediction interval is always wider than the confidence interval of the mean response because of the added uncertainty involved in predicting a single response versus the mean response.

please like;)

Add a comment
Know the answer?
Add Answer to:
12.4 For each of the following, explain what is wrong and why. (a) (1m) A 95%...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • If I were to construct intervals using the same data set and point estimators from a...

    If I were to construct intervals using the same data set and point estimators from a normal distribution, which of these intervals would have the greatest width? Why did you choose that one? a) A 95% confidence interval for the mean μ b) A 99% confidence interval for the mean μ c) A 95% prediction interval for a future observation d) A 99 % prediction interval for a future observation

  • For each of the following, explain what is wrong and why. a) If b 1 =...

    For each of the following, explain what is wrong and why. a) If b 1 = 5 in a logistic regression analysis with one explanatory variable, we estimate that the probability of an event is multiplied by 5 when the value of the explanatory variable increases by one unit. b) The intercept b 0 is equal to the odds of an event when x = 0 . c) The odds of an event are 1 minus the probability of the...

  • 27. For a party with 55 people invited, which of the following is true? The median...

    27. For a party with 55 people invited, which of the following is true? The median arrival time would be exactly 62.899999999999991 minutes. b. The median arrival time would be 62.899999999999991 minutes on average. The median arrival time would be more than 63 minutes. d. We are not able to estimate the median arrival time for this party as all parties are different. a e. None of the above. 28. What is the relationship between a prediction interval and a...

  • N Two intervals are given, A and B, for the same value of the explanatory variable....

    N Two intervals are given, A and B, for the same value of the explanatory variable. N A: 88 to 100; B: 93 to 95; N i (a) Which interval is the confidence interval for the mean response? ni Which interval is the prediction interval for the response? (b) What is the predicted value of the response variable for this value of the explanatory variable? Enter the exact answer. The predicted value is exact number, no tolerance Click if you...

  • Explain what ​"95​% ​confidence" means in a 95​% confidence interval. What does ​"95​% ​confidence" mean in...

    Explain what ​"95​% ​confidence" means in a 95​% confidence interval. What does ​"95​% ​confidence" mean in a 95​% confidence​ interval? A. If 100 different confidence intervals are​ constructed, each based on a different sample of size n from the same​ population, then we expect 95 of the intervals to include the parameter and 5 to not include the parameter. B. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 95​%....

  • 2.81 What’s wrong? Each of the following statements contains an error. Describe each error and explain...

    2.81 What’s wrong? Each of the following statements contains an error. Describe each error and explain why the statement is wrong. A negative relationship is always due to causation. A lurking variable is always a quantitative variable. If the residuals are all negative, this implies that there is a negative relationship between the response variable and the explanatory variable.

  • Suppose that you have in your possession bivariate data giving birthrate and life expectancy information for...

    Suppose that you have in your possession bivariate data giving birthrate and life expectancy information for a random sample of 15 countries. For each of the countries, the data give both x, the number of births per one thousand people in the country's population, and y, the country's female life expectancy in years. The least squares regression equation computed from your data is y = 84.06 -0.51x. Suppose that you're predicting the female life expectancy for a country whose birthrate...

  • Explain what is meant by the statement, "We are 95% confident that an interval estimate contains...

    Explain what is meant by the statement, "We are 95% confident that an interval estimate contains μ" Choose the correct answer below. O A. The statement reflects the confidence in the particular interval found from this application. It explains that over many repetitions of this O B. The statement reflects the confidence in the estimation process rather than in the particular interval that is calculated from the sample ° C. The statement reflects the confidence in the particular interval found...

  • Explain what is meant by the statement, "We are 95% confident that an interval estimate contains...

    Explain what is meant by the statement, "We are 95% confident that an interval estimate contains μ" Choose the correct answer below. A. The statement reflects the confidence in the particular interval found from this application. It explains that there is a 95% chance that the O B. The statement reflects the confidence in the particular interval found from this application. It explains that over many repetitions of this O C. The statement reflects the confidence in the estimation process...

  • 0 2 10 0 2 8 Consider the multiple regression model where є¡ ~ iid Ņ(0, σ*) for i = i, 2, 3, 4, 5...

    0 2 10 0 2 8 Consider the multiple regression model where є¡ ~ iid Ņ(0, σ*) for i = i, 2, 3, 4, 5. (c) Fill in the values for the following ANOVA table: Source of Variation Sum of Squares df Mean Square F Regression on Xi, X2 Error Total (Corrected) (d) State the nul and alternative hypotheses associated with the F test from the ANOVA table in part (c) and do the F test (e) Compute R2 (f)...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT