Question 15 In the below residual plot, which assumption(s) of regression is/are violated? Residuals vs Fitted 2 4 Residuals -20 880 049 8 88 08 o 0 810 300 -8 -6 -4 -2 0 2 4 6 Fitted values Linear relationship between X and Y Equal variance across levels of X Normality Residuals are independent
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![Question 15
In the below residual plot, which assumption(s) of regression is/are violated?
Residuals vs Fitted
2
4
Residuals
-20
880
049
8
88
08
o
0
810 300
-8
-6
-4 -2 0 2
4
6
Fitted values
Linear relationship between X and Y
Equal variance across levels of X
Normality
Residuals are independent](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ef95ec8-11bc-441a-b20b-806b03b8bf91%2F75b7d3dc-4e4b-4966-bbc4-595f1cb5a3dd%2Fj9xhq1v_processed.jpeg&w=3840&q=75)
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- d) Hence test whether ? is significant. Give reasons for your answer.You want to look at an ANOVA table of a regression in which a dependent variable is predicted using an intercept and one slope coefficient. Unfortunately, as you want to look at the table, you knock over your coffee mug which smudges out some of the numbers. Here is what you still can read: • n=7 • F-ratio = 15 • Residual sum of squares (RSS) = 16 • t-score of the slope coefficient = 3.873 How big is the explained sum of squares (ESS)? a 44 b 52 c 48 d 40 How big is the total sum of squares (TSS)? a 64 b 52 c 60 d 56 How big is the explained R-squared? a 0.7 b 0.75 c 0.8 d Cannot be determined What's the p-value for the F-ratio? a 0.012 b 0.024 c 0.036 d…Which of the following is not a condition that needs to be assessed in multiple linear regression? o residuals are normally distributed observations are independent of each other residuals have constant variation o explanatory variables are linearly related with each other o high correlation among explanatory variables
- What percentage of the variation in can be explained by the corresponding variations in and taken together?Hi, please help with this assignment. Please show the work step by step as I am having trouble understanding how to compute them.What is dependent and independent variables? Fully write out the regression equation.What is the sample size used in this investigation? Fill in the blanks identified by ‘*’ and ‘**’. Is β significant, at the 5% level of significance?
- Brain size Does your IQ depend on the size of yourbrain? A group of female college students took a test thatmeasured their verbal IQs and also underwent an MRI scan to measure the size of their brains (in 1000s of pix-els). The scatterplot and regression analysis are shown, and the assumptions for inference were satisfied.Dependent variable is: IQ_VerbalR-squared = 6.5% s = 21.5291 df = 18Variable Coefficient SE(Coeff)Intercept 24.1835 76.38Size 0.098842 0.0884a) Test an appropriate hypothesis about the associationbetween brain size and IQ.b) State your conclusion about the strength of thisassociation.Q3 An automobile engineer claim that his team has successfully designed a new engine that saves more car fuel than the previous designs. He wishes to prove that by conducting on road experiment to compare both designs. A sample of 40 cars of previous and new engines version were involved in the experiment. The data of fuel consumption (liter/100km) were recorded in Table Q3. Table Q3 Data of fuel consumption (liter/100km) Mean Variance Previous version New version 5.9 0.017 5.4 0.022 (a) State the type of data collection involved in the given case study. Justify your answer. (b) Construct 90% confidence interval for the different mean between previous and new engine version. (c) Suppose the sampling for both engine versions were reduced to 15. Test the engineer claim at 0.05 significance level.Why is the equation of the regression line for this scatter plot ?
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