Given the data as shown in the table below X Y 3.1 10.2 2.6 8.7 3.7 9.1 1.8 7.8 3.4 8.7 The correct equation of the "Best-Fit"/Regression line associated with the given data above would be Oŷ = 6.8162 + 0.7136 Oy = 0.71367 + 6.8162 Oŷ = 0.71362 + 6.8162 Oŷ = 0.7136x + 6.8162 Oy = 0.7136z + 6.8162
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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- The average midterm score in a large statistics class was 65 with an SD of 15. The average final score in the same class was 70 with an SD of 10. The correlation coefficient between midterm and final scores was r=0.6. Using the regression line, we predict the final score of a student with a midterm score of 80 to be , but this prediction is likely to be off by about . Fill in the blanks, rounding each answer to one decimal point.The average midterm score in a large statistics class was 65 with an SD of 15. The average final score in the same class was 70 with an SD of 10. The correlation coefficient between midterm and final scores was r-0.6. Using the regression line, we predict the final score of a student with a midterm score of 80 to be but this prediction is likely to be off by aboutUsing the regression line attached. Based on only the above plot, one can conclude: a) height causes an increase in weight b) weight causes an increase in height c) taller people are more likely to weigh more than shorter people, at least in the sample on which this data is based d) a statistically significant predictive relationship between height and weight e) c and d
- Suppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…Is there a linear correlation between students' high school GPA and their current GPA (College GPA)? 1. Let's try to test this claim by using the survey. Assume that alpha is 0.05. 2. What is the equation of the regression line? 3. What is the best-predicted GPA if the high school GPA is 3.5?A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.185 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.185 + 0.007x and standard deviation 0.005. (You may need to use a table.) b)What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.29 µm? (c)Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.281? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of less than 0.286? (Round your answer to four decimal places.)
- A paper suggests that the simple linear regression model is reasonable for describing the relationship between y = eggshell thickness (in micrometers, µm) and x = egg length (mm) for quail eggs. Suppose that the population regression line is y = 0.125 + 0.007x and that ?e = 0.005. Then, for a fixed x value, y has a normal distribution with mean 0.125 + 0.007x and standard deviation 0.005. (a) What is the mean eggshell thickness for quail eggs that are 15 mm in length? ____ µm What is the mean eggshell thickness for quail eggs that are 17 mm in length? ____ µm (b) What is the probability that a quail egg with a length of 15 mm will have a shell thickness that is greater than 0.23 µm? _____ (c) Approximately what proportion of quail eggs of length 14 mm have a shell thickness of greater than 0.222? (Hint: The distribution of y at a fixed x is approximately normal. Round your answer to four decimal places.) ____ Approximately what proportion of quail eggs of length…Suppose the following data were collected relating the selling price of a house to square footage and whether or not the house is made out of brick. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average brick houses are more expensive than other types of houses at the 0.010.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence." Price Sqft Brick (1 if brick, 0 if otherwise 241255 3392 0 184518 2038 1 176488 1906 0 240068 3329 0 169760 1828 0 185335 2081 0 172735 1926 0 224281 3425 0 172589 1676 1 214635 2735 1 199666 2373 1 208348 2662 1 218360 2834 1 230160 3254 0 164812 1431 0 191560 1839 1 203255 2456 1 173325 1530 0 168073 1381 1 179620 1457 1 Selecting a checkbox will replace the entered answer value(s) with the checkbox value.…Suppose the following data were collected relating the selling price of a house to a square footage and whether or not the house is made out of wood. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average wood houses are more expensive than other types of houses at the 0.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence" Selling Prices of Houses Price Sqft Wood (1 if wood, 0 if otherwise) 198637 2197 1 204780 2490 1 204200 2596 0 209184 2779 0 196696 2378 0 221429 2988 1 223290 3385 1 156740 1360 1 177254 1985 0 180533 1916 0 187262 1957 1 234023 3378 0 229634 3327 0 207475 2695 0 209448 2596 1 207347 2732 0 191976 2061 1 199300 2310 1 199943 2499 0 207985 2574 1 Selecting a checkbox will replace the entered answer value(s) with the checkbox value. If…
- 10)A sample of 100 bears was treated like it was the whole population of Jellystone Park bears, and the mean weight was found to be 800 pounds with standard deviation 9 pounds, the mean blood pressure was 150 with standard deviation 12, and the sample correlation coefficient of weight with blood pressure was found to be .6. Based on this information, what is the regression slope for the SLR equation for predicting blood pressure using observed weight for Jellystone bears? .35 .20 .80 NONE OF THE OTHERS .40Bill is the office manager for a group of financial advisors who provide financial services for individual clients. She would like to investigate whether a relationship exists between the number of presentations made to prospective clients in a month and the number of new clients per month. The following table shows the number of presentations and corresponding new clients for a random sample of six employees. Employee Presentations New Clients 1 2 1 2 8 2 3 9 4 4 10 3 5 11 5 6 12 6 Bill would like to use simple regression analysis to estimate the number of new clients per month based on the number of presentations made by the employee per month. The average number of new clients per month for an employee who made 20 presentations per month is ________. 5.02 5.45 3.43 8.69Suppose that a sample of n = 12 pairs of X and Y scores has SSY = 90 and a Pearson correlation of r = +0.40. Does the regression equation predict a significant portion of the variance? Test with α = .05.(hint: SStotal = SSY; r2 = SSregression/SSTotal)