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 C 95 63 D 70 56 E 70 42 F 35 26 A) The estimated regression equation for this data is ŷ = 25.401 + 0.296x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use ? = 0.05. Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = B) Test for a significant relationship using the F test. Use ? = 0.05. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = C) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
| Brand | Price ($) | Score |
|---|---|---|
| A | 180 | 74 |
| B | 150 | 69 |
| C | 95 | 63 |
| D | 70 | 56 |
| E | 70 | 42 |
| F | 35 | 26 |
A) The estimated regression equation for this data is
where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use ? = 0.05.
| Source of Variation |
Sum of Squares |
Degrees of Freedom |
Mean Square |
F | p-value |
|---|---|---|---|---|---|
| Regression | |||||
| Error | |||||
| Total |
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