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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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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?For these (x,y) pairs of data points: 1,5 3,7 4,6 5,8 7,9 Compute . Compute . What is the equation of the regression line?Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 5 9 14 Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). y^= + x Use the estimated regression equation to predict the value of y when x = 5 (to 1 decimal).y^ =
- Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual starting salary of an employee with a doctorate degree? (Someone with no work experience). $ What is the predicted bi-annual starting salary of an employee with a bachelor’s degree? (Someone with no work experience). $Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.
- The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks obtained in the exam in POLI 308 (Y). POLI 344 (X)8 8 9 10 10 11 12 13 13 11 14 POLI 443 (Y) 7 11 8 7 12 11 10 12 14 17 15 (i) State the two equation lines of the regression line. (ii) If a student was absent from POLI 443 but scored 18 in POLI 344 (X) state the regression line, which would be suitable for estimating his/her possible mark in POLI 443 and work out a fair estimate for his /her possible mark.Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 6 11 13 Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = (e) Use the estimated regression equation to predict the value of y when x = 2.A set of n = 4 pairs of X and Y values has a Pearson correlation of r = 0.60 and SSY = 200. The standard error of estimate for the regression equation is _______. a. 8 points b. 10 points c. 6 points d. 4 points
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.4 6.6 3.9 2.4 2.4 2.2 0.6 yy 14 10.9 9.4 7.5 6 5.8 5.8 4.4 xx = thousands of automatic weaponsyy = murders per 100,000 residents Use excel to determine the equation of the regression line. (Round to 2 decimal places)Determine the regression equation in y = b0 + bx(x) form and write it below. A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons? B) How many murders per 100,000 residents can be expected in a state with 2.1 thousand automatic weapons?A set of n = 15 pairs of X and Y values has a correlation of r = +0.80 with SSY = 75, and the regression equation for predicting Y is computed. Find the standard error of estimate for the regression equation. How big would the standard error be if the sample size were n = 30.The owner of Original Italian Pizza restaurant chain wants to understand which variable most strongly influences the sales of his specialty deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of several outlets in central Indiana. These data are provided in the file P10_04.xlsx. Estimate a simple linear regression equation between the quantity sold (Y) and each of the following candidates for the best explanatory variable: average price of deep-dish pizzas (X1), monthly advertising expenditures (X2), and disposable income per household in the areas surrounding the outlets (X3). Round your answers for intercept coefficients to the nearest whole number and slope coefficients to two decimal places, if necessary. If your answer is negative number, enter "minus" sign.