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- 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.What kind of plot is useful for deciding whether finding a regression line for a set of data points is reasonable?Please help me to write the interpretation for ANOVA and linear regression for both countries in Austria and United Kingdom (Attachment is there)
- Online clothes II For the online clothing retailer dis-cussed in the previous problem, the scatterplot of Total Yearly Purchases by Income showsThe correlation between Total Yearly Purchases and Incomeis 0.722. Summary statistics for the two variables are: a) What is the linear regression equation for predictingTotal Yearly Purchase from Income? b) Do the assumptions and conditions for regression ap-pear to be met? c) What is the predicted average Total Yearly Purchasefor someone with a yearly Income of $20,000? Forsomeone with an annual Income of $80,000?d) What percent of the variability in Total YearlyPurchases is accounted for by this model?e) Do you think the regression might be a useful one forthe company? Comment.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…Let the Explanatory Variable represent the age of a sample of seven randomly selected men. Let the Response Variable represent the corresponding cholesterol measurements of these men. Explanatory Variable: 39, 52, 47, 43, 63, 58, 69 Response Variable: 189, 238, 220, 215, 244, 236, 248 (a) What is the equation of the regression line for this sample data? The y-intercept of your equation must be to three decimal places and the slope of your equation must be to four decimal places. A. y = 2.1664x + 142.336 B. y = 1.8653x + 105.698 C. y = 1.7283x + 135.543 (b) Using the equation of your regression line from (a) above what is the predicted cholesterol measurement when a man is 60 years old? Your answer must be to four places. A. 239.2410 B. 272.3200 C. 217.6160
- Burger King 2010 revisited Recall the Burger Kingmenu data from Chapter 7. BK’s nutrition sheet listsmany variables. Here’s a multiple regression to predict calories for Burger King foods from Protein content (g),Total Fat (g), Carbohydrate (g), and Sodium (mg) perserving:Dependent variable is CaloriesR-squared = 99.8, R-squared (adjusted) = 99.8,s = 8.51 with 111 - 5 = 106 degrees of freedomSource Sum ofSquares df MeanSquare F-RatioRegression 4750462 4 1187616 16394Residual 7678.64 106 72.4400Variable Coefficient SE(Coeff) t-Ratio P-ValueIntercept -5.826 2.568 -2.27 0.0253Protein 3.8814 0.0991 39.1 60.0001Total fat 9.2080 0.0893 103 60.0001Carbs 3.9016 0.0457 85.3 60.0001Na/Serv. 1.2873 0.4172 3.09 0.0026 a) Do you think this model would do a good job of predict-ing calories for a new BK menu item? Why or why not? b) The mean of Calories is 453.9 with a standard devia-tion of 234.6. Discuss what the value of s in the re-gression means about how well the model fits the data. c) Does…Does more education lower a person’s level of prejudice? The number of years of education and the score on a prejudice test for ten people is given in the following table. Higher scores on the test indicate more prejudice. Years of Education: 12, 15, 14, 13, 18, 10, 16, 12, 10, 4Score of Prejudice Test: 1, 6, 2, 3, 2, 4, 1, 5, 5, 10 The regression equation is calculated to be y' = 10.5 - 0.532x. After conducting a hypothesis test, your decision is to reject the null hypothesis. Predict the value of y' when x=11. 10.5 4.645 1.945 0.749What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below: Least Squares Linear Regression of PRICE Interpret the standard deviation of the regression model. a) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values. b) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model. c) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56. d) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
