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- If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 pointsAssume that variables xx and yy have a significant correlation, and that the line of best fit has been calculated as ˆy=1.4x+3.6y^=1.4x+3.6. One observation is (9,16.3)(9,16.3).What is the predicted value of yy for the value x=9x=9? What is the residual for the value x=9x=9? What is the best interpretation for the residual? The value 16.316.3 is below the average value for yy when x=9x=9 The value 99 is above the average value for yy when y=16.3y=16.3 The value 16.316.3 is above the average value for yy when x=9x=9. The value 16.316.3 is below the average value for xx when y=16.3
- Here is a bivariate data set.x y71 461 555 6148 -876 3126 7074 -62 Find the correlation coefficient and report it accurate to four decimal places.r =A random sample of nonindustrialized countries was selected, and the life expectancy in years is listed for both men and women. Men 61.7 42.8 72.6 57.9 55.4 62.1 Women 50.4 74.2 75.3 75.4 49.1 65.2 The correlation coefficient for the data is =r−0.003 and =α0.05. Should regression analysis be done? Now Find the equation of the regression line. Round the coefficients to at least three decimal places. =y′+abx =a =b Now Find women's life expectancy in a country where men's life expectancy =60 years. Round your answer to at least three decimal places. Women's life expectancy is ____ years.The birth lengths in cm (x) and birth weights in kg (y) of a sample of 50 newborn female babies are compared, yielding a correlation coefficient of r=0.578 and a linear regression equation of ŷ =−8.89+0.243x The babies all had lengths between 46.5 and 53.0 cm, and weights between 2.50 and 4.05 kg. Based on this, predict the birth weight of a newborn female baby with a birth length of 48.5 cm.
- A sample of sunshine (x) in percent and temperature in O Fahrenheit (y) is recorded below to perform a linear regression test for whether or not correlation exists at α = .05. Assume test conditions are satisfied. x 28.6 32.1 35 31.6 28.6 30 26.6 33.2 24.2 31.3 y 75.4 91.3 86.9 90.7 85.8 88.3 72.5 86.4 70.7 89.4 What is the regression equation and what is the value of y^y^ when x = 25?Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y= annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid ? .The correlation between the two variables is ? .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is ? . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…
- Compute for the necessary correlational analysis based on the given data. The following data, adapted from Montgomery, Peck, and Vining (2001), present the number of certified mental defectives per 10,000 of estimated population in the United Kingdom ( y) and the number of radio receiver licenses issued (x) by the BBC (in millions) for the years 1924 through 1937. Fit a regression model relating y and x. Comment on the model. Specifically, does the existence of a strong correlation imply a cause-and-effect relationship?Given that the means of x and y are 64 and 66 , their standard deviations are 2.8 and 3.2 respectively and the coefficient of correlation between them is 0.5. 1) write down the regression lines.2. The following data, adapted from Montgomery, Peck, and Vining (2001), present the number of certified mental defectives per 10,000 of estimated population in the United Kingdom ( y) and the number of radio receiver licenses issued (x) by the BBC (in millions) for the years 1924 through 1937. Fit a regression model relating y and x. Comment on the model. Specifically, does the existence of a strong correlation imply a cause-and-effect relationship?