Question

In: Math

The paired data ((x, y)): (1,6),(5,8),(7,9),(8,0),(4,1) is considered. (a) Find the pearson correlation coefficient (b) Find...

The paired data ((x, y)): (1,6),(5,8),(7,9),(8,0),(4,1) is considered.

(a) Find the pearson correlation coefficient

(b) Find the slope and intercept of the regression coeffients.

(c) What percent of the variation in y is described by variation in x?

Some statistics are not resistant to a single outlier. An example would be the mean value, as one extremely large of small value can tip the scales. Which of these statistics is also not resistant to outliers: median, standard deviation, IQR, range, Pearson correlation, linear regression coefficients?

Expert Solution

(a) Find the pearson correlation coefficient

correlation coefficient r = -0.16

(b) Find the slope and intercept of the regression coeffients.

y = -0.2333x + 5.9667

slope = -0.2333

Intercept = 5.9667

(c) What percent of the variation in y is described by variation in x?

The coefficient of determination, r², is a measure of how well the variation of one variable explains the variation of the other, and corresponds to the percentage of the variation explained by a best-fit regression line which is calculated for the data

R² = 0.0245

so 2.45% of the variation y is described by variation in x?

Which of these statistics is also not resistant to outliers:

Outliers are calculate based on the IQR

IQR is measured from quartile 3 and quartile 3.

Quartile 3 - Quartile 1 = IQR

Apart from IQR all other statistics mentioned are not resistant to outliers

milcah answered 4 months ago

1) What is the sum ∑ X Y? 2) What is the Pearson correlation coefficient (r)...

1) What is the sum ∑ X Y? 2) What is the Pearson correlation coefficient (r) for the data below? 3)If you were to test the Pearson correlation coefficient for significance, what would be the critical value of t (alpha=.05)? 4) If you were to test the Pearson correlation coefficient for significance, what would be the computed value of t (alpha=.05)? 5)If you were to test the Pearson correlation coefficient for significance, what would be your conclusion (alpha=.05)? 6) For...

Using the data below find the linear correlation coefficient. x y xy

Using the data below find the linear correlation coefficient. x y xy x2 y2 3 4 12 9 16 4 6 24 16 36 5 7 35 25 49 7 12 84 49 144 8 14 112 64 196 ___________________________________________ 27 43 267 163 441 Also, utilizing the above data, find the slope and intercept.

Determine the Pearson product-moment correlation coefficient for the following data. x 1 10 9 8 5...

Determine the Pearson product-moment correlation coefficient for the following data. x 1 10 9 8 5 3 2 y 10 4 4 5 7 7 10 (Do not round the intermediate values. Round your answer to 3 decimal places.) Correlation coefficient, r = ___ The Y values are actually: Y 9 4 4 5 7 7 8

1. Determine the Pearson product-moment correlation coefficient for the following data. x 1 11 9 7...

1. Determine the Pearson product-moment correlation coefficient for the following data. x 1 11 9 7 4 3 2 y 10 4 4 5 7 7 8 Correlation coefficient, r = enter the Correlation coefficient rounded to 3 decimal places 2. People in the aerospace industry believe the cost of a space project is a function of the mass of the major object being sent into space. Use the following data to develop a regression model to predict the cost...

12.1 Determine the Pearson product-moment correlation coefficient for the following data. x 1 11 9 7...

12.1 Determine the Pearson product-moment correlation coefficient for the following data. x 1 11 9 7 5 3 2 y 9 4 6 5 7 7 8 (Do not round the intermediate values. Round your answer to 3 decimal places.) Correlation coefficient, r = enter the Correlation coefficient rounded to 3 decimal places

To compute a Pearson correlation coefficient, data must be measured on an ordinal scale. true or...

To compute a Pearson correlation coefficient, data must be measured on an ordinal scale. true or false Scatter plots give a visual representation of the strength and direction of the correlation coefficient true or false When you have significant results in data analysis, it is customary to report all relevant means and standard deviations. true or false

a. Describe what the Pearson correlation coefficient is and what the coefficient of determination is. compare...

a. Describe what the Pearson correlation coefficient is and what the coefficient of determination is. compare it to a real world example or a example problem

Let X and Y have the joint distribution shown in the table. Find the correlation coefficient....

Let X and Y have the joint distribution shown in the table. Find the correlation coefficient. (round to 4 decimal digits) p(x,y) x/y 1 2 3 1 0.12 0.08 0.11 2 0.18 0.14 0.07 3 0.17 0.05 0.08

Conduct a Pearson correlation coefficient test (r) using the following data: A researcher is interested in...

Conduct a Pearson correlation coefficient test (r) using the following data: A researcher is interested in studying the relationship between team fandom and social perception. She asks participants how much they love the Los Angeles Dodgers and then asks another participant in the same study how cool they think that person is. The data is as follows, and is on an 11-point scale: Participant Fandom Perception A 10 11 B 1 1 C 9 10 D 10 10 E 5...

For the following data, calculate the correlation coefficient. (Show the code) Y X 72 45 73...

For the following data, calculate the correlation coefficient. (Show the code) Y X 72 45 73 38 75 41 76 35 77 31 B.Plot the scatterplot of the data above AND add the scatterplot here. (Show code) What type of relationship do you see? Using the information from problem 1 calculate the intercept and coefficient. Then write the regression equation to explain the relationship. (Show the code) Interpret the R-squared.