The heights of a sample of 10 fathers and their eldest sons are given below : 167 162 Height of fathers (X) Height of son (Y) (i) Compute the regression of Y on X. (ii) Compute the correlation coefficient. (ii) Compute the coefficient of determination and give your comments. 170 193 167 166 169 171 164 165 168 167 166 166 168 165 168 170 165 168
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- 4. For a sample of 12 observations, a businessman wants to regress the price (in dollar) of the laptop (Y) on the processor's speed (X). The summary results of the observations are given below. Σx = 19.8 , Σy = 24798, Σxy = 431882 Σx^2 = 3388, Σγ^2 = 57365692 a) compute correlation coefficient (b) Find the fitted regression line of the price of laptop on processor speed.The ages (X) of ten second-hand cars and their km values (Y) are given below.a) Calculate the correlation coefficient between X and Y.b) Calculate the coefficients of the regression line of the Y with respect to X.c) Estimate the km value of a 5.0 year old car. X and Y values given in the picture.A sample of n = 15 pairs of X and Y scores produces a Pearson correlation of r = 0.45, SSY = 90. a) If the regression equation was found for these scores, how much of the Y variability would be predicted by the regression equation (SSregression) and how much would not be predicted (SSresidual)? b) Does the regression equation predict a significant portion of the variability for the Y scores? (Equivalently, is the Pearson correlation significant?)
- Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using alpha equals 0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of theseals? Overhead Width 7.1 7.6 9.7 9.3 8.6 8.2 Weight 115 197 243 198 197 186The average gasoline price per gallon (in cities) and the cost of a barrel of oil are shown below for a random selection of weeks in 2015 . Oil ( $ ) Gasoline ( $ ) 47.79 2.638 44.62 2.636 81.08 2.944 43.67 2.528 40.58 2.623 48.64 2.682 The correlation coefficient for the data is =r0.954 and =α0.01. Should regression analysis be done? Find the equation of the regression line. Round the coefficients to at least three decimal places. =y′+abx =a =b Find the cost of gasoline when oil is $57 a barrel. Round the answer to at least three decimal places. When oil is $57 a barrel, gas costs $ per gallon.Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Overhead width overhead weight 7.1 111 7.6 164 9.8 250 9.2 192 8.8 205 8.2 183 Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? The linear correlation coefficient is r=? (Round to three decimal places as needed.) The linear correlation coefficient is r=? (Round to three decimal places as needed.) The critical values are r=? (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute value of the linear correlation coefficient is ______ than the positive critical value, there _______ sufficient evidence to support the claim that there is a linear…
- The following data gives the information on the ages (in years) and the number of breakdownsduring the past month for a sample of 7 machines at a large industrial company.Age (X) 12 7 2 8 13 9 4Number of breakdowns (Y) 9 5 1 4 11 7 2(a) Draw a scatter diagram to represent the above data.(b) Calculate the value of Pearson’s correlation coefficient r. Interpret the value of r.(c) Calculate coefficient of determination. Interpret your answer.(d) Determine the equation of the regression line using least squares method.(e) What is the expected breakdown for an eleven year old machine?Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.6 9.6 9.2 8.7 8.2 Weight 113 173 242 192 200 188 PLOTS INSERTED AS PICTURE The linear correlation coefficient is r=________. (Round to three decimal places as needed.) The critical values are r=________. (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute value of the linear correlation coefficient is ▼ less greater than the positive critical value, there ▼ is not is sufficient evidence to support the claim that there is a…In a partially destroyed laboratory, record of an analysis of correlation, data, the following results only are legible:Variance of X=9. Regression equation: 8X –10Y + 66=0, 40X–18Y = 214.(1) the mean value X and Y,(2) the correlation coefficient between X and Y, and (3) the standard deviation of Y ?
- 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?From the data of the following table: Calculate Spearman's rank correlation coefficient between x and y and determine its type. sHere 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.