A study was performed on wear of a bearing y and its relationship to x1 = oil viscosity and x2 = load. The following data were obtained. y 293 230 X₁ 1.6 15.5 X₂ 851 816
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- A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of regressions coefficients and write down the simple linear regression model.The raw material used in the production of a synthetic fiber was stored in a place that had no humidity control. Measurements of the relative humidity in the storage place and the water content of a sample of the raw material (both in percentages) in 12 days gave the following results:x = Humidityy = water content a) Create a scatter plot to verify that it is reasonable to assume that the regression of Y on x is linear.b) Fit a straight line using the method of least squares.c) Find a 95% confidence interval for the mean water content of the raw material, when the humidity of the storage place is 40%.d) Find the 95% prediction limits for the water content of the raw material, when the humidity of the storage place is 40%.A consumer buying cooperative tested the effective heating area of 20 differentelectric space heaters with different wattages. Here are the results. a. Compute the correlation between the wattage and heating area. Is there a direct oran indirect relationship?b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient isgreater than zero. Use the .05 significance level.c. Develop the regression equation for effective heating based on wattage.d. Which heater looks like the “best buy” based on the size of the residual?
- From the article “Association of cognitive functioning with retinal nerve fiber layer thickness” by van Koolwijk et al., in Investigative Ophthalmology & Visual Science, October 2009, Vol. 50, No. 10, below is table 2 showing the results of fitting several multiple linear regression models for different response variables. Write down the fitted model corresponding to the last row of the table. You can leave the intercept as hatB0. Interpret the coefficient values corresponding to the RNFL Thickness and Male variables.Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient.A group of 13 healthy children and adolescents participated in a phycological study designed to analyze the relationship between age and average total sleep time (ATST). To obtain a measure for ATST (in minutes), recordings were taken on each subject on three consecutive nights and then averaged. Results are provided to you in Sleep&Age.xlsx Download Sleep&Age.xlsx file. (2 points) Determine the least-squares regression line for predicting average total sleep time using age. (2 points) Make a scatter plot of the data with ATST on the y-axis (vertical axis) and Age on the x-axis (horizontal axis) with least squares regression line overlaid on the top (i.e.: obtain the fitted line plot). Make sure to attach the plot below. (7 points) Check the assumptions for the simple linear regression. Attach any plots you used check the assumptions and comment on them. (7 points) We want to see if the average sleep time decreases as the children grow older. Write the appropriate null and…
- Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?The number of disk drives (in millions) made at aplant in Taiwan during the past 5 years a) Forecast the number of disk drives to be made next year, usinglinear regression.b) Compute the mean squared error (MSE) when using linearregression.c) Compute the mean absolute percent error (MAPE).A research department of an American automobile company wants to develop a model topredict gasoline mileage (measured in MPG) of the company’s vehicles by using theirhorsepower and weights (measured in pounds). To do this, it took a random sample of 50vehicles to perform a regression analysis as follows: SUMMARYOUTPUTRegression StatisticsMultiple R 0.865689R Square 0.749417Adjusted RSquare 0.738754Standard Error 4.176602Observations 50ANOVAdf SS MS FRegression a 2451.973702 1225.987 dResidual b 819.8680976 cTotal 49 3271.8418CoefficientsStandardError t StatIntercept 58.15708 2.658248208 21.87797Horsepower -0.11753 0.032643428 -3.60028Weight -0.00687 0.001401173 -4.90349(a) State the multiple regression equation. Interpret the meanings of the coefficients forhorsepower and weight.(b) Test the validity of this multiple regression equation at the significance level of 1%. Showyour reasoning.(c) The research department claims that the weight of the vehicle is negatively linearly related…
- Part of the ANOVA summary table for using efficiency ratio (X1) and total risk-based capital (X2) to predict ROAA is shown to the right. The results also state that SSRX1=3.7902 and SSRX2=3.7615. a. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the most appropriate regression model for this set of data. Write the hypotheses for the contribution of the variable efficiency ratio.A random sample of 8 office staffs hired within the previous year was selected from a large corporation. For each selected office staff, his or her experience (in months) at the time of hire and starting salary were recorded. The data is given in the table below. Experience (in months) 13 6 8 10 20 7 9 15 Starting Salary (in thousand pesos) 20 14 16 19 21 12 13 21 Determine the following: regression equation sum of squares for error standard error coefficient of determinationThe ols() method in statsmodels is used to fit a simple linear regression model using “Exam4” as the response variable and “Exam3” as the predictor variable. The output is shown below. A text version is available. What is the correct regression equation based on this output? Is this model statistically significant at 10% level of significance (alpha = 0.10)? Select one. (Hint: Review results of F-statistics) Exam4 = 68.9576 + 0.1028 Exam3, model is statistically significant Exam4 = 76.85 + 0.206 Exam3, model is not statistically significant Exam4 = 68.9576 + 0.1028 Exam3, model is not statistically significant Exam4 = 76.85 + 0.206 Exam3, model is statistically significant