Subject: STATISITCS

Question 1: Suppose a study is conducted to investigate the relationship between the scores students receive on their Midterm and nal tests. Based on the following sample, find the correlation coefcient : Mid Final 180 280195 280210 300225 316240 320255 350255 370264 320265 400290 350 a 0.566 b 0.645 c 0.738 d 0.802 e 0.905 Question 2: The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable. True or False Question 3: The following assumption about the error term is incorrect a Errors are normally distributed b The mean of error terms is zero c Error terms have a constant variance d Error terms depend on the explanatory variable e Errorterms are uncorrelated across observations Question 4: The Least Squares Regression minimizes the sum of a). deviations between actual and predicted Y values b). squared deviations between actual and predicted X values c). absolute deviations between actual and predicted Y values d). absolute deviations between actual and predicted X values e). squared deviations between actual and predicted Y values Question 5: The coefcient of Determination only indicates the strength of the relationship between the independent and dependent variables but does not reveal the direction of the relationship (positive or negative). True or False Question 6: When using simple regression analysis, if there is a strong correlation between the independent and dependent variables, we can conclude that an increase in the value of the independent variable is associated with an increase in the value of the dependent variable. True or False Question 7: The standard error of the estimate is the sample estimated standard deviation of the explanatory variable (X). True or False Question 8: The sample estimate of the variance of error in a Regression model is a. MSE b. bo c. b1 d. SSE e. SSxy Question 9: A merchant needs a forecast for the sales of a product (in millions). He thinks that the sale is affected by expenditure on advertising (in millions of dollars). Based on the data set with six observations, the summary statistics are given below (X is expense on advertising expenditure in million dollars and Y is number of products sold in millions): [X = 24; [Y = 42; [X2 = 124; EY2 = 338; EXY = 196 Find the Intercept and slope, write the Regression Equation, and interpret the results. Make a forecast for the sale of products (in millions) if the advertising expenditure is 5 million dollars. Calculate the correlation coefficient, coefficient of Determination. Verify the relationship between the coefficient of correlation and the coefficient of Determination. Calculate SSE and MSE and standard error of the slope coefficient and perform the test of significance. Blank Question 10: A product rating agency has the following data about the quality score for an electronic product and respective prices for 10 popular brands. Brand Price Score A 2900 55 B 2800 54 C 2700 45 D 3500 56 E 3300 54 F 2000 35 G 4200 68 H 3100 56 1 2500 32 J 3000 45 Calculate the Regression coefficients based on the above data and explain what the values indicate. Measure the Goodness of Fit using the Coefficient of Determination and interpret the calculated value with respect to the model's overall explanatory power. Also check the relationship between R2 and r. (show how to solve in excel)