. In a trivariate distribution. o, = 3, o, = 4, 0, = 5 r, = 0.4, r,, = 0.6 r,, = 0.7 %3D Determine the regression equation of X. on X, and X, if the variates are measured frem their means.
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- Using 23 observations on each variable, a computer program generated the following multiple regression model. y = 65.5 +9.56x1+3.27x2-4.23x3– 9.23x4 If the standard errors of the coefficients of the independent variables are, respectively, 3.44, 2.30, 2.76, and 4.99, can you conclude that the independent variable x, is needed in the regression model? Let B1, B2, Ba denote the coefficients of the 4 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 to determine your 4 .../ answer. (a) State the null hypothesis H, and the alternative hypothesis H,. H, : 0 H, : 0 (b) Determine the type of test statistic to use. Degrees of freedom: D=0 OSO (c) Find the value of the test statistic. (Round to two or more decimal places.) O#0 OO (d) Find the two critical values at the 0.10 level of significance. (Round to two or more decimal places.) | and || (e) Can you conclude that the independent variable is needed in the regression model? Yes No 미The slope D of the sample regression line provides a measure of O1.the change in the population value of the dependent variable for every unit change In the Independent varlable. O 2. the change in the population average value of the dependent varlable for overy unit change in the independent varlable, 03.the change In the population value of the independent varlable for every unit change in the dependent varlable. 04.the change in the population average value of the independent variable for every unit change in the dependent varlablo. O 5.the change in the estimated population value of the dependent variable for every unit change in the Independent varlable. O 6.the change in the estimated population average value of the dependent variable for every unit change in the independent varlable. O 7. the change in the estimated population value of the independent variable for every unit change in the dependent variable, O 8. the change in the estimated population average value of the…Given are 3 observations for two variables, x and y. 1 3 6. 9. 10 What is the estimated regression equation? Select one: a. ÿ = -2 + 6.5x O b. ý 10.89 – 0.87x с. у -0.87+ 10.89x d. ŷ 6.5 – 2x %3D
- a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point with coordinates (2,3), use the pairs of values for the remaining 9 points and find the equation of the regression line. c. Compare the results from parts (a) and (b). 02468100246810xy A scatterplot has a horizontal x-scale from 0 to 10 in increments of 1 and vertical y-scale from 0 to 10 in increments of 1. Ten points are plotted with nine points, (4, 6), (5, 6), (6, 6), (4, 7), (5, 7), (5, 7), (6, 7), (4, 8), (5, 8), and (6, 8), forming a square and the tenth point (2, 3) being below and to the left of the square. Question content area bottom Part 1 a. What is the equation of the regression line for all 10 points? y=enter your response here+enter your response herex (Round to three decimal places as needed.) Part 2 b. What is the equation of the regression line for the set of 9 points? y=enter your response…A researcher would like to predici the dependent variable Y fram the two independent variables X, and Xg for a sample of N = 18 subjecis. Use muliple linear regression to calculate the coefficient of multiple determination and Lest the significance of the overall regression model. Use a significance level a = 0.01. Y 53.2 42.4 56.6 75 32.2 62.9 68.2 26.9 70.1 63 30.9 57,4 52 44.2 70.1 52.9 33 55.9 67.8 35.3 54.9 51.1 49 47.8 39.5 57.4| 46.9 45.7| 52.7 60.5 57.2 43.2 61.1 40.4 42 | 45,7 56.1 42.2 37.3 51.8 | 58.9 53,4 51.9 42.2 47.5 37.1 48 46.8 66 33.8 | 61.7 32.3 53.4 57.5 F= Pvalue - What is your decision for the hypothesis test? O Reject the null hypothesis, H.:B, = B =0 O Fail to reject H, What is your final conclusion? O The evidence supports the claim that one ar more of the regression coefficients is non-zero O The evidence supports the claim that all of the regression coelfficients are zero OThere is insufficient evidence to support the claim that at least one of the regression…eBook Given are five observations for two variables, z and y. 15 13 17 19 51 58 50 23 16 The estimated regression equation for these data is y= 62.15 - 2.05z. a. Compute SSE, SST, and SSR. %3D SSE (to 2 decimals) SST (to 2 decimals) SSR (to 2 decimais) b. Compute the coefficient of determination r, Comment on the goodness of fit. (to 3 decimals) The least squares line provided an Select your answer it; % of the variability in y has been explained by the estimated regression equation (to 1 decimal). c. Compute the sample correlation coefficient. Enter negative value as negative number. (to 3 decimals) 0 Jcon Key 4 Question 2 of
- 7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannelThere is a relationship between the following variables as y = a + b * (1 / x).Determine the regression coefficients (a and b) of the regression equation.Calculate the correlation coefficient and interpret the degree of correlation by comparing the calculated correlation coefficient with the critical correlation coefficient for 1% significance level, taking into account the number of data. Estimate the y-value for x = 0.8 and the x-value for y = 3.5 x 0,58 0,5 0,32 0,18 0,15 0,1 y 1,2 1,5 2 3 4 5From the scatter plot, which of the following is TRUE? Scatterplot of Apartment Price vs Distance Apartment Price (in RM 1000) 250 225 200 175 150 0 1 Distance from Commercial Area (km) O a. We can conclude a significant linear relationship between apartment price and distance from the commercial area at a 1% significance level. regression line, the smaller the r. O b. The value of the coefficient of correlation is negative.
- Given are five observations for two variables, z and y. z 3 9 10 18 20 | 53 55 50 14 16 The estimated regression equation for these data is y 70.38 – 2.73z. a. Compute SSE, SST, and SSR. SSE (to 2 decimals) 230 (to 2 decimals) (to 2 decimals) b. Compute the coefficient of determination. Comment on the goodness of fit. SST SSR (to 3 decimals) The least squares line provided an pood explained by the estimated regression equation (to 1 decimal). c. Compute the sample correlation coefficient. Enter negative value as negative number. % of the variability in y has been (to 3 decimals)Given the correlation coefficient 0.794 and the linear regression equation ŷ = 16.4 +1.58x, compute the coefficient of determination. p² Round to 4 decimal places. =