Calculate the following: a. Compute the value of correlation coefficient Ⓡ. What is the least-squares equation? C. If student 11 has an IQ = 130, what is his/her estimated entrance exam score? b.
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- In a study measuring the relationship between height in centimeters and annual income in dollars, it has been determined that for Group 1, r2 =0.15 and for Group 2, r2 =0.10 where r denotes the correlation between the two variables. Least-squares regression lines are fitted to the observations from each group. Which of the following statement is true: A. There could be a positive relationship between the two variables for Group 1 and a negative relationship between the two variables for Group 2 B. The sum of the residuals for Group 1 is greater than the sum of the residuals for Group 2. C. Measuring the height in inches would increase the value of r2 for both groups. D. None of the answer options is true Can you also explain the difference between r and r2, and why least square regressions are used?The following data shows the yearly income (in $1000) and age of a sample of seven individuals. Income (in $1000) Age 20 18 24 20 24 23 25 34 26 24 27 27 34 27 Develop the least squares regression equation. Estimate the yearly income of a 30-year old individual. Compute the coefficient of determination. Use a t test to determine whether the slope is significantly different from zero. Use level of significance as 0.05.Here is a bivariate data set.xy182425915011737106295223812246 Find the correlation coefficient and report it accurate to four decimal places. r =
- The following table shows how many weeks a sample of 6 persons have worked at an automobile inspection station and on any given day: a) Find the least squares estimators and the values for a and b ??? = ___________ ? = ___________ ??? = ___________ ? = ___________ ??? = ___________ b) Determine AND WRITE the equation for the best fit line. c) Find the correlation coefficient, r, and describe the relationship between weeks in the program and time improvement.The following summary statistics resulted from a study of the relationship between the cost ofa barrel of crude oil (x) and the price of a gallon of regular unleaded gasoline (y).n = 12x 241.1 y 14.34 4,932.82 x 17.288 2 y xy 291.55(1) Compute the sample correlation r and use it to judge the strength of linear relationshipbetween x and y.(2) Obtain the equation of the least squares line, and interpret its slope and intercept.(3) Predict the price of a gallon of regular unleaded gasoline when the cost of a barrel of crudeoil is 50.The following data shows the yearly income (in $1000) and age of a sample of seven individuals. Income (in $1000) Age 20 18 24 20 24 23 25 34 26 24 27 27 34 27 a. Develop the least squares regression equation. b. Estimate the yearly income of a 30-year old individual. c. Compute the coefficient of determination. d. Use a t test to determine whether the slope is significantly different from zero. Use level of significance as 0.05.
- Consider the following data: Fit a line, y = x1 + x2t, to the data using the least squares approach.The following table shows the annual sales revenue of 12 firms and their expenditure on the market research. Sales revenue (£ 000) Expenditure on market research (£ 000) 24 1.2 20 0.8 18 1.1 14 0.8 19 0.9 13 0.5 25 1.3 26 1.5 30 1.4 34 1.6 24 1.2 20 0.8 Calculate the Pearson correlation coefficient between the two variables, to two…Here is a bivariate data set. x y -2.6 120.6 30.5 34.9 40.1 85.3 18.2 82.2 14.8 89.6 21.8 69.3 36.3 49.9 49.1 25.7 32.3 56.6 52.2 -8.4 Use technology to find the correlation coefficient and report it accurate to three decimal places.
