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- Sir Francis Galton, in the late 1800 s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of variables such as the size of parents and the size of their offspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest (adult) son. The data are given in tabular form and also displayed in the scatter plot below, which gives the least-squares regression line as well. The equation for this line is y =95.35 +0.48 x Height of Height of son, father, x (in centimeters) centimeters) y (in 175.8 178.1 193.5 190.3 210. 183.2 176.6 173.3 171.1 200- 183.8 186.5 190. 175.8 175.6 180 159.8 167.2 xx 170 155.5 175.8 162.0 172.1 160- 190.9 188.0 150 180.1 187.1 Tdo ito Ido 130 200 z1o 186.9 177.5 171.5 181.5 Height of father, x (in centimeters) 190.5 195.7 201.0…Which of the following statements is true? a. None of the suggested answers are correct b. If the coefficient of determination is 0.64, the correlation coefficient must be 0.80. c. An indication of a nonlinear relationship between two variables would be a coefficient of correlation equal to zero. d. The strength of the correlation between two variables depends on the sign of the coefficient of correlation. e. The t-test for the true slope ?1=0 is identical to the t-test for the true correlation ?=0 only for large samples.A departmental store has the following sales for a period of last one year of 8 salesmen, who have different years of education. Years of Education 8 10 10 12 14 16 Annual Sales (Thousand Tk.) 100 120 80 100 80 100 70 130 a. Determine the correlation coefficient r between the two variables. Answer rounded to at least 4 decimal places. b. Determine the slope coefficient B1 for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. c. Determine the y-intercept Bo for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. d. What will be the annual sales when the years of education is 11 (years)? Answer rounded to at least 4 decimal places. Thousand Tk.
- Q.4. Obtain the equation of the line of regression of y on x from the following data and estimate the blood pressure when the age is 50 years. Age in years x Blood pressure y 50 142 40 120 71 162 35 110 60 140 45 125 52 155 47 140 36 111 40 135 65 150 59 153The mortality rate of a sample of the population as a function of daily tobacco consumption can be seen below: Number of cigarettes "x": 3 5 6 15 20 Mortality rate "y" : 0.2 0.3 0.4 0.5 0.7 With these data, solve the following: a. Determine and interpret the correlation coefficient. b. Find the regression line of y on x. c. What will be the mortality rate for a consumer of 40 cigarettes per day?2. I surveyed 150 adults in the U.S. and asked them how many hours of TV the watched on average per week. I then ran a regression of # of hours of TV on whether or not they were a college graduate (=1 if yes, =0 if no), their age in years, the number of children in their household, and whether or not they live a cold climate (=1 if latitude is greater than 41.2, =0 otherwise). The results fro the regression are shown in the table below. Estimate p-value College Graduate -0.8 0.003 Age 0.1 0.150 Number of Children 0.10 0.521 Cold Climate 1.8 0.047 Intercept -1.23 0.041 (a) What is the dependent variable in this regression? (b) What are the independent variable(s) in this regression? (c) What is the unit of analysis? (d) What is the sample size? (e) What is one binary variable used in this analysis? (f) What is one ratio variable used in this analysis? (g) What is the predicted number of TV hours watched by a 50 year old, colleg graduate, with no children at home who lives in Arizona…
- The following table shows the number of units of a certain item sold by a store over a month in terms of the price in dollars charged by the store. Price in dollars 0.90 1.00 1.15 1.25 1.40 Number sold . 315 280 230 215 195 Use technology to find the correlation coefficient for the data. (Use decimal notation. Give your answer to two decimal places.) correlation coefficien What type of correlation is there between the price and the number sold?21. Which of the following statements is true regarding the sources of variation present in an analysis of regression? SSy is partitioned into variation explained by the regression model and residual variation. If most of the variability in Y is associated with residual variation, then X predicts Y. There are three sources of variation in an analysis of regression: regression variance, residual variance, and error variance. Regression variation measures variability in X, whereas residual variation measures variability in Y.An econometric model is a multiple linear regression model if Question 10Select one: a. it explains the average value of y as a linear function of several explanatory variables b. it explains the sample mean of y as a function, linear in the parameters , of several x c. it explains y as a linear function of several x , the explanatory variables d. it explains the average of y as a function of several x e. none of the answers is correct
- y: 30 -10 50 10 1 25 -15-60 15 8 35 20-5 7. 10 9. -40 -5 X: 9. 3 4 6. 0.05. Test for significant positive (linear) correlation at a =8. The table depicted below lists randomly selected students' self-reported hours of studying (x) and their corresponding final grades (y). a. Find the correlation coefficient r. b. Find the critical value. c. Is there a linear correlation (i.e., can Họ be rejected)? d. Find the regression equation. X 30 37 10 18 7 15 y 93 100 75 88 72 86
