**Regression Analysis with Outliers: Understanding Correlation**A student uses the following dataset to compute a least-squares regression line and determine the correlation coefficient:\[\begin{array}{c|ccccccc}x & 0.7 & 0.8 & 1.7 & 1.7 & 1.3 & 2.6 & 8.0 \\\hliney & 1 & 2 & 2 & 1 & 0 & 1 & 5 \\\end{array}\]The student's task is to evaluate whether the regression line effectively illustrates the relationship between the explanatory variable \(x\) and the response variable \(y\).### Evaluation Question:Is the student's claim correct that the regression line provides an excellent explanation of the relationship?### Response Options:- **Option 1:** - **No,** because the outlier is inflating the correlation coefficient.- **Option 2:** - **No,** because the slope of the regression line is only 0.54.- **Option 3:** - **Yes,** because \( r^2 = 0.74 \) means that 74% of the variation in \( y \) is explained by the least-squares regression of \( y \) on \( x \).- **Option 4:** - **Yes,** because the correlation coefficient is \( r = 0.86 \), which is close to 1.### Discussion:The key points to consider include the impact of outliers on the correlation coefficient, the significance of the slope in describing the fit of the regression line, and the interpretations of \( r^2 \) and \( r \).

Here, sample size 'n' is 7. The linear regression line is given by: x y x2 y2 xy 0.7 1 0.49 1…

A student uses the given set of data to compute a least-squares regression line and a correlation coefficient: 0.7 0.8 1.7 1.7 1.3 2.6 8.0 y 1 2 1 1 5 The student claims that the regression line does an excellent job of explaining the relationship between the explanatory variable x and the response variable y. Is the student correct? No, because the outlier is inflating the correlation coefficient. No, because the slope of the regression line is only 0.54. Yes, because r2 = 0.74 means that 74% of the variation in y is explained by the least-squares regression of y on x. Yes, because the correlation coefficient is r = 0.86, which is close to 1. 2.

A student uses the given set of data to compute a least-squares regression line and a correlation coefficient: 0.7 0.8 1.7 1.7 1.3 2.6 8.0 y 1 2 1 1 5 The student claims that the regression line does an excellent job of explaining the relationship between the explanatory variable x and the response variable y. Is the student correct? No, because the outlier is inflating the correlation coefficient. No, because the slope of the regression line is only 0.54. Yes, because r2 = 0.74 means that 74% of the variation in y is explained by the least-squares regression of y on x. Yes, because the correlation coefficient is r = 0.86, which is close to 1. 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, y = b0 + b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 23 26 31 40 48 Number of Bids 3 4 6 7 9 Table Step 5 of 6: Find the error prediction when x = 31. Round your answer to three decimal places.
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 106 108 117 181 193 Number of Bids 10 15 16 17 18 Table Find the estimated y-intercept and correlation coefficient ..Round your answer to three decimal places.
A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N = 19 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level a = 0.02. X, X2 50.6 43.6 44.6 31.4 49.4 44.3 41.6 50.7 43 29.2 44.2 25 18.9 31.7 38.6 47.5 47.3 52.2 47.8 36 72 29.2 58.4 72.5 33.4 40.5 49.2 29.9 54 52.5 46.1| 56.9 35.7 70.8 - 10.7 -5.4 45.5 33.6 21.1 60.9 46.6 59.3 38.7 84.6 53.3 49.2 54 49.5 51.4 66.9 17.4 45.5 53.3 42.7 69.6| 86.8 SS.eg F = P-value = What is your decision for the hypothesis test? O Reject the null hypothesis, Ha: B = B = 0 O Fail to reject Ho What is your final conclusion? O The evidence supports the claim that one or more of the regression coefficients is non-zero O The evidence supports the claim that all of the regression coefficients are zero O There is insufficient evidence to support the claim that at…
A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in meter square and income is measured in IDR millions. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Which of the independent variables in the model are significant at the 5% level? Formulate the hypothesis and explain the answer. How far can you rely upon this model? Or, what is the percentage variation in House explained by the model? What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of IDR 400 million and having a family size of 4?
The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, y = bo + b₁x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Completion Percentage 58 60 61 62 65 Interception Percentage 5 4.5 4 3.5 3 Table Copy Data Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable ŷ. Tables Keypad Keyboard Shortcuts Next
Can you help me out by showing me an example of a weak positive correlation scatter plot? with a relistic example that shows the two variables that demonstrate this pattern?
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 20 30 35 42 49 Number of Bids 3 4 5 6 9
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 124 143 158 160 196 Number of Bids 12 13 15 16 20 Table Step 2 of 6 : Find the estimated y-intercept. Round your answer to three decimal places.
A company wishes to estimate a regression line for the relationship between sales and advertising. а. To arrive at its decision regarding the best model to use, the company has calculated the following three correlation coefficients. i. ii. The sales in any month depend on that month's advertising with r = 0.28 The sales in any month depend on 50% of the previous month's advertising and 50% of that month's advertising with r= 0.68 The sales in any month depend on the previous month's advertising with r = 0.92 iii. Interpret each of the above correlation coefficients and state which of the suggested models you would choose as the basis for predicting sales. Justify your answer.
A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. a. Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is 8.6 cars. b. Compute the coefficient of determination and interpret its meaning. The coefficient of determination is 0.234 Therefore, about _________% of the variation in monthly sales is explained by the years of sales experience. (Type an integer or decimal rounded to one decimal place as needed.)
I need correct only handwritten otherwise skip pls