The accompanying Minitab regression output is based on data that appeared in the article "Application of Design of Experiments for Modeling Surface Roughness in Ultrasonic Vibration Turning."* The response variable is surface roughness (um), and the independent variables are vibration amplitude (um), depth of cut (mm), feed rate (mm/rev), and cutting speed (m/min), respectively. The regression equation is Ra- -0.972 - 0.0312a + 0.557d + 18.31 + 0.00282v Predictor Coef SE Coef ConaTADE 0723 0.3923 0.015
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A: Given: n=14∑yi=572∑yi2=23530∑xi=43∑xi2=157.42∑xiyi=1697.80
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- We collected teacher ratings for 25 courses taught by an instructor over a sis-year period. The students ratings of the instructor are on a scale of 1 to 9. We found that The linear regression equation is Anerape Rating 7.88-0.068 Numer of Studenta 1interpret the slope of this model including units The average rating decreases * per each additional student 2. The predicted teacher rating for a class size of 15 students using the givem prediction equation 6.86 6.18 Tiext page CS Scanned with CamScannerA student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 answer please : 1: Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.Fit these three regression models and then discuss the similarities and differences between them, particularly as relates to slope estimates (use CI’s) and R2. Also address why this is a “special case” and we wouldn’t necessarily expect to see these model characteristics for a typical dataset. a) Additive model including both predictors (output attached) b) Model including only Moisture (output attached) c) Model including only Sweetness BrandLiking = 68.62 + 4.38 Sweetness Term 95% CI P-ValueConstant (50.16, 87.09) 0.000Sweetness (-1.46, 10.21) 0.130 S R-sq R-sq(adj)10.8915 15.57% 9.54%
- The Conde Nast Traveler Gold List for 2012 provided rating for the top 20 small cruise ships. The data from annual Readers’ Choice Survey are the overall scores(Y) each ship received based on several criteria, including Itineraries/Schedule (X1), Shore Excursions(X2), and Food/Dinning(X3). The estimated regression equation to predict the overall scores is Y= 35.6184+0.1105 X1+0.2445 X2+0.2474 X3. Part of the regression results is shown below. Coefficients Standard Error Intercept 35.6184 13.2308 Itineraries/Schedule(X1) 0.1105 0.1297 Shore Excursions(X2) 0.2445 0.0434 Food/Dinning(X3) 0.2474 0.0621 Use the T test to determine whether or not the coefficient of X1 is significant. Use Level of significance=.05? Be sure to state null and alternative hypotheses.…Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The regression model was Y= total sales (thousands of dollars), X₁ = display floor space (square meters). X₂ competitors' advertising expenditures (thousands of dollars), X3 = advertised price (dollars per unit). Predictor Intercept FloorSpace Competing Ads Price Coefficient 1,287.26 11.52 -6.934 -0.1476 (a) Write the fitted regression equation. (Round your coefficient Competing Ads to 3 decimal places, coefficient Price to 4 decimal places, and other values to 2 decimal places. Negative values should be indicated by a minus sign.) ý= 1,287 26 + 11:52 *FloorSpace + (6.934) CompetingAds + (0.1446) * PriceThe article "The Undrained Strength of Some Thawed Permafrost Soils" contained the accompanying data on the following. y shear strength of sandy soil (kPa) x₂-depth (m) x₂ water content (%) The predicted values and residuals were computed using the estimated regression equation 9-145.41-14.24x, +12.70x₂ +0.079x,-0.236 +0.441x where x₂-x₂²x₂-x₂², and x ₁2 Y 14.7 *2 9.1 31.6 48.0 36.5 27.1 25.6 36.7 25.8 10.0 6.0 39.2 16.0 7.0 39.3 16.8 7.0 38.4 20.7 7.4 34.0 38.8 8.3 33.7 16.9 6.4 28.0 27.0 8.1 33.0 16.0 4.6 26.4 24.9 9.8 37.9 7.3 2.8 34.5 12.8 1.9 36.3 Predicted y Residual 23.83 47.07 26.46 10.77 14.57 16.88 23.38 25.07 16.23 24.31 15.06 28.64 15.08 8.15 -9.13 0.93 -0.86 -0.77 1.43 -0.08 -2.68 13.73 0.67 2.69 0.94 -3.74 -7.78 4.65 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO- 1x |x SSResid- SSRegr - Ix (b) Calculate R² for this regression model. (Round your answer to three decimal places.) R²-X How would you…
- please interpret the modelThe article "The Undrained Strength of Some Thawed Permafrost Soils"+ contained the accompanying data on the following. y = shear strength of sandy soil (kPa) x₂ = depth (m) x₂= water content (%) The predicted values and residuals were computed using the estimated regression equation ŷ-140.14 13.15x₁ + 12.22x₂ + 0.070x3 -0.227x4 + 0.413x5 where x3 = x₁²₁x4x₂², and x = x1x2. y X1 14.7 8.8 31.6 48.0 36.7 27.1 x2 25.6 36.7 25.8 10.0 6.0 39.0 16.0 6.8 39.1 16.8 7.0 38.4 20.7 7.2 33.8 38.8 8.5 33.7 16.9 6.6 27.0 7.9 33.0 7.3 27.8 16.0 4.6 26.2 24.9 10.0 37.7 2.8 34.5 12.8 2.1 36.5 Predicted y 23.92 46.76 26.79 11.42 14.23 16.77 23.03 25.48 16.21 24.09 15.00 29.13 14.88 7.79 Residual -9.22 1.24 -1.19 -1.42 1.77 0.03 -2.33 13.32 0.69 2.91 1.00 -4.23 -7.58 5.01 (a) Use the given information to calculate SSResid, SSTO, and SSRegr. (Round your answers to four decimal places.) SSTO= SSResid= SSRegr = (b) Calculate R² for this regression model. (Round your answer to three decimal places.) R² = How…Consider the accompanying data set of dependent and independent variables a. Perform a general stopwise regression using a 0.05 for the p-value to enter and to remove independent variables from the regression model b. Perform a residual analysis for the model developed in part a to verify that the regression conditions are met Click the icon to view the data a. Use technology to perform the general stepwise regression What is the resulting regression equation? Note that the coefficient is 0 for any variable that was removed or not significant -0.69 (050), (050)+(018) - X (Round to two decimal places as needed) • Data Table: y 63 43 51 49 40 42 23 37 30 27 20 31 FR 74 63 78 3534 52 44 47 35 17 15 20 17 Print X₂ 21 259. 15 9 38 18 17 5 40 27 30 33 x₂ 22 aadosa 2NNG 29 20 17 13 17 8 15 10 10 Done 1
- A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. What can you say about the strength of this relationship? Carry out a test to determine whether y is…The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920X2 (a) Interpret b₁ in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a…A group of Maternal and Child Health public health practitioners are interested in the relationship between depression and a number of health outcomes. Suppose the research team gathers information on a group of participants, and constructs a multiple linear regression model looking at the relationship between depression and household income dichotomized as above and below the federal poverty line controlling for a number of potential confounders. The following is a computerized output displaying the results of their analysis. Parameter Estimate Standard Error t Value Pr > |t| Intercept 0.2617346843 0.09209917 2.84 0.0046 Income (1/0) -.1962038300 0.04574793 -4.29 <.0001 Race (W or AA) -.0320329506 0.03900447 -0.82 0.4118 bmicontinuous 0.0051185980 0.00216986 2.36 0.0186 Alcohol (Y/N) -.0088735044 0.03090631 -0.29 0.7741 A) What are the independent and dependent variables? B) Which potential…