95 59 70 56 70 42 35 24 The estimated regression equation for this data is - 23.398 + 0.306x, where x- price ($) and y= overall score. Does the t test indicate a significant relationship between price and the overall score? Use a- 0.05. State the null and alternative hypotheses. O Ha: o-0 H: Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value -
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).
Brand
Price ($)
Score
A
180
74
B
150
69
95
59
70
56
70
42
F
35
24
(a) The estimated regression equation for this data is ý = 23.398 + 0.306x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: Bo = 0
H: Bo + 0
O Ho: B, = 0
O Ho: B1 + 0
H: B1 = 0
O Ho: B, 20
H: B, < 0
O Ho: Bo *0
H: Bo = 0
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
O Do not reject Hn. We cannot conclude that the relationship between price ($) and overall score is significant.
O Reject H.. We cannot conclude that the relationship between price ($) and overall score is significant.
O Do not reject Hn. We conclude that the relationship between price ($) and overall score is significant.
O Reject H.. We conclude that the relationship between price ($) and overall score is significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd757ee9f-b4c9-4f09-b9d8-5ad7d1fae788%2F8b080b24-60a2-4fda-9a3e-e42466e84f59%2Flbfmez8_processed.png&w=3840&q=75)
![(b) Test for a significant relationship using the F test. Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B, + 0
H: B, = 0
O Ho: B = 0
H: B, + 0
O Ho: Bo +0
H: 80 = 0
O Ho: Bq20
H: B, < 0
O Ho: Bo = 0
H: Bo + 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
P-value =
What is your conclusion?
O Do not reject H.. We conclude that the relationship between price ($) and overall score is significant.
O Reject H. We conclude that the relationship between price ($) and overall score is significant.
O Reject H.. We cannot conclude that the relationship between price ($) and overall score is significant.
O Do not reject H,. We cannot conclude that the relationship between price ($) and overall score is significant.
(c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)
Source
Sum
Degrees
of Freedom
Mean
of Variation
of Squares
Square
p-value
Regression
Error
Total](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd757ee9f-b4c9-4f09-b9d8-5ad7d1fae788%2F8b080b24-60a2-4fda-9a3e-e42466e84f59%2Fn6zycg_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)