Problem 5 True or Fal a) If the correlation coefficient lr= ± 1, then all the da

Question

Problem 5 True or Fal a) If the correlation coefficient lr= ± 1, then all the data points lie exactly on a straight line. T F b) The correlation coefficient r is a number that indicates the direction and the strength of the relationship between the dependent variable y and the independent variable >x c) If the correlation coefficient 0, then there is no linear relationship whatsoever between the dependent variable y and the independent variable x d) The standard deviation is a measure of the linear relationship between two quantitative variables T e)The best fitting line relating the dependent variable y to the independent variable x, often called the regression or least-squares line, is found by minimizing the sum of the squared differences between the data points and the line itself. f) The scatterplot is a graph that is used to graphically represent the relationship between two quantitative variables TF g) If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane generally moving from the lower left corner to the upper right corner. T F h)If two variables have a correlation coefficient equal to 0.005, this means that there is no relationship between the two variables i) A perfect correlation between two variables will always produce a correlation coefficient of+ T F T F T F TF T F

Explanation / Answer

Solution:

Part a) True.

Since r = + 1 indicates there is perfect positive correlation , In such case all points are line on straight line , y increases when x increases.

similarly for r = -1 , there is perfect negative correlation , In such case all points are line on straight line , y decreases when x increases.

Part b) True ,
correlation coefficeint gives extent of linear relationship between two variables. sign of the correlation coefficient r gives direction of relationship , that is if r is negative , there is negative correlation and in this case as x increases , y decreases and if r is positive , there is positive correlation and in this case as x increases , y increases.

and value of the r gives strength of relationship between two variables and it is in between -1 to +1.

If r is close to + ot - 1 , then there is strong correlation and if r is close to 0 there is weak or no correlation.

Part c) True.
Since if r = 0 , there is no correlation between two variables. In this case as x increases, sometimes y increases , sometimes y decreases or sometimes y remains constant for any change of x value.
Thus there is exact direction in change in y , when x changes. Thus when r = 0 , there is no relationship between two variables.

Part d) False.

Standard deviation is the measure of dispersion. It gives average amount dispersion in the data from mean value.

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