Q3: Multiple regression using Minitab. interpret the results in bullets step by step Regression Analysis: y versus x1, x2 Regression Equation
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- The linear regression alanysis shows that the pressure, measured in millibars is the explanatory variable, and the wind speed, measured in miles per hour is the reponse variable. The scatter plot shown below represents wind speed contrasted with the pressure in a hurricane, each dot in the scatter plot represents a hurricane. This figure reveals that there is a negative linear association between the two variables with a sample correlation coefficient of r = -0.9498. y = -1.095x + 1152.3 is the regression model that is used to describe the relationship between the two variables, the slope is a = -1.095, the y-intercepts is b = 1152.3, and the coefficient of determination is ?2 = 0.9022. The slope reveals that as the atmospheric pressure increases by one milibar, the predicted speed of wind will decrease by -1.095. Analysing the coefficient of determination displayed in the figure below, ?2 = 0.9022 means that approximately 90% of the variability on wind speed is explained by the…can ridge regression be applied if sample size is smaller than the number of predictors?The average height of a large group of children is 43 inches, and the SD is 1.2inches. The average weight of these children is 40 pounds, and the SD is 2pounds. The correlation between the two variables is r = 0.65.A scatter diagram is drawn, with height on the horizontal axis and weight on thevertical axis. The scatter diagram is football shaped. The regression line forpredicting weight based on height is drawn through the scatter.(a) Predict the weights and the typical size of the error for those predictions ineach of the following case:A child who is 43 inches tall is predicted to weigh _____________ pounds, give ortake _____________ pounds.A child who is 41.8 inches tall is predicted to weigh ____________ pounds, give ortake _____________ pounds.
- The average height of a large group of children is 43 inches, and the SD is 1.2inches. The average weight of these children is 40 pounds, and the SD is 2pounds. The correlation between the two variables is r = 0.65.A scatter diagram is drawn, with height on the horizontal axis and weight on thevertical axis. The scatter diagram is football shaped. The regression line forpredicting weight based on height is drawn through the scatter.(a) Predict the weights and the typical size of the error for those predictions ineach of the following case:A child who is 43 inches tall is predicted to weigh _____________ pounds, give ortake _____________ pounds.A child who is 41.8 inches tall is predicted to weigh ____________ pounds, give ortake _____________ pounds. 37 pounds and is 41.8 inches tall. Relative to allchildren with the same height, this child’s weight is (pick one)(i) smaller than average(ii) about average(iii) larger than average(iv) impossible to determineShow your work and justify…he average height of a large group of children is 43 inches, and the SD is 1.2 inches. The average weight of these children is 40 pounds, and the SD is 2pounds. The correlation between the two variables is r = 0.65.A scatter diagram is drawn, with height on the horizontal axis and weight on the vertical axis. The scatter diagram is football-shaped. The regression line forpredicting weight based on height is drawn through the scatter.Q. Predict the weights and the typical size of the error for those predictions ineach of the following case: Suppose a child’s height is at the 29th percentile of all heights. Using regression, our best guess is that the child’s weight (measured in pounds) is at the___________________ percentile compared to all other children.Aggregate data were collected for a recent year in 44 Denver neighborhoods on various demographic measures, including the crime rate (# of crimes per 1000 population). A multiple linear regression was used to build a predictive model predicting crime rate from four of these neighborhood characteristics: population size, % of children in the population, % of participation in free school lunch, and % change in household income over recent years. A portion of the ANOVA table from this model is below. Analysis of Variance Sum of DF Squares Mean Source Square F Value Pr>F Model 299771 74943 <.0001 Error Corrected Total 43 473806 Provide the 5 values that have been omitted from this table. Specifically, provide: df(model), df(error), SS(error), MS(error), and the F statistic. Include intermediate calculations wherever used.
- You may need to use the appropriate technology to answer this question. The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. Analysis of Variance SOURCE DF Adj SS Regression 1 41587.3 Error 7 Total 8 51984.1 Predictor Coef SE Coef T-Value Constant 20.000 3.2213 6.21 X 7.210 1.3626 5.29 Regression Equation Y = 20.0 + 7.21 X (a) How many apartment buildings were in the sample? (b) Write the estimated regression equation. ŷ = (c) What is the value of sb1? (d) Use the F statistic to test the significance of the relationship at a 0.05 level of significance. State the null and alternative hypotheses. H0: ?1 ≠ 0Ha: ?1 = 0H0: ?0 = 0Ha: ?0 ≠ 0 H0: ?0 ≠…Interpret the assocfation between agea nd math scores in the univariate regression model, and is the association between them significant? How much variance in math score is explained by age in the univariate regression model?a sample of 60 grade 9 student age was obtained to estimate the mean age of all grade 9 students. x = 15.3 years and the population variance is 16
- 8 Interpret the stationarity, ACF, and PACF for both residuals plot . Include what AR or ARMA model it should beLast school year, the student body of a local university consisted of 35% freshmen, 25% sophomores, 24% juniors, and 16% seniors. A sample of 300 students taken from this year's student body was taken to determine if there had been a significant change in % of students for each classification for this year as compared to last year. This analysis is an example of a Regression O Goodness of Fit Analysis of Variance Test of IndependenceThe final test and exam averages for 20 randomly selected students taking a course in engineering statistics and a course in operations research follow. Assume that the final averages are jointly normally distributed.Find the regression line relating the statistics final average to the OR final average.(c) Estimate the correlation coefficient.
