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- Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?1. Plot the data points on a scatter diagram. 2. Determine the equation of the regression line and find Pearson product-moment correlation coefficient. 3. Determine the point estimate of y at x = 5.5on the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?
- 8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .400024) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
- 1) Indicate whether the following statements are true or false. Explain why and show your work. c) In the regression Y= B1+ B2X + B3Z+u , if there is a strong linear correlation between X and Z, then it is more likely you fail to reject the null hypotheses that individual slope parameters are insignificant.5.1 Determine the equation of the relationship between the predictor variable (x) and the response variable (y). 5.2 What does the simple linear regression equation obtained in question 5.1 indicates on every 1 km/hr increase in speed? 5.3 Using the simple linear regression equation obtained in question 5.1, estimate the total fuel expenditure of a randomly selected driver of one of the newly launched Volvo trucks who drove at an average speed of 100 km/hr during a 900 km haulage. 5.4 Determine the Pearson Correlation Coefficient.uppose IQ scores were obtained from randomly selected couplescouples. For 2020 such pairs of people, the linear correlation coefficient is 0.8900.890 and the equation of the regression line is ModifyingAbove y with caret equals negative 0.74 plus 1.02 xy=−0.74+1.02x, where x represents the IQ score of the husbandhusband. Also, the 2020 x values have a mean of 101.17101.17 and the 2020 y values have a mean of 102.7102.7. What is the best predicted IQ of the wifewife, given that the husbandhusband has an IQ of 9999? Use a significance level of 0.05. The best predicted IQ of the wifewife is nothing. (Round to two decimal places as needed.
- The fish in my pond have mean length 14.73 inches with a standard deviation of 2.27 inches and mean weight 4.83 pounds with a standard deviation of .8 pounds. The correlation coefficient of length and weight is .6. If the length of a particular randomly selected fish is reported to be 17 inches, and if we use simple linear regression to predict the weight of a fish whose length is reported to be 15.8 inches long, then what is the expected squared error?1.The head of the production department of a RM Electronic Company wants to determine the relationship between the number of workers who assemble the product and the number of units assembled per day. d.Test whether the correlation is significant at 5% level of significance. e.Determine the regression line. f.Predict the number of units used if there are 20 workers. g.How many workers is needed to produce 1000 units per day?17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…