Concept explainers
(a)
Construct a
(b)
Find the value of
Find the value of
Find the value of b.
Find the equation of the least-squares line.
Construct the line on the scatter diagram.
(c)
Find the sample
Find the value of the coefficient of determination
Mention percentage of the variation in y is explained by the least-squares model.
(d)
Check whether the claim that the population
(e)
Find the change in the crime rate for a neighbourhood with
(f)
Verify the values of
(g)
Find the 80% confidence interval for the change in crime rate when the percentage change in population is
(h)
Check whether the claim that the slope
(i)
Find a 80% confidence interval for
Interpret the confidence interval.
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Understandable Statistics: Concepts and Methods
- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.arrow_forwardYou are given below the following information about advertising and sales. Adv. Exp. (X) (S Lakhs) Sales (Y) Lakhs) Мean 10 90 S.D. 3 12 Correlation Coefficient 0.8 (a) Calculate the two regression lines. (b) Find the likely sales when advertisement expenditure is (c) What should be the advertisement expenditure if the company wants to attain a sales target of 15 lakhs. 120 lakhs ?arrow_forwardThe following three problems refer to the data sets displayed below: b 11.If the slope of the least squares regression line is negative, what else must be negative? a) The correlation (r)? b) The coefficient of determination (r)? c) The y-intercept (bo) d) More than one of the above must be negative. e) None of the above need be negative.arrow_forward
- Question 3. a) A Biologist is comparing intervals (m seconds) between the matting calls of a certain species of tree frog and the surrounding temperature (t degree Celsius). The following results were obtained: t 8 13 14 15 15 20 25 30 6.5 4.5 4 3 2 1 1. Fit the regression line in the form m = a + bt. 2. Interpret your estimates. 3. Use your regression line interval between matting calls when the surrounding temperature is 10 degrees. (6 marks) estimate the timearrow_forwardSuppose two variables are under study are temperature in degrees Fahrenheit (y) and temperature in degrees centigrade (x). The regression line for this situation is y = 9/5X +32. Assuming there is no error in observing temperature, What is the expected correlation coefficient in this given scenario. Answer:arrow_forwardFor a certain data set the regression equation is y = 2 + 3.5x. The correlation coefficient between y and x in this data set is positive must be 3 O is negative must be 1 must be 0arrow_forward
- A large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth. a) Explain how this is related to the concept of Panel Data. b) Explain how you could estimate the relationship between wealth and child labour using pooled OLS, Random Effect (RE), Fixed Effect (FE) estimators. Write down the estimation equations and the conditions needed to guarantee consistency. Compare the FE and the OLS estimators: Is either of these two estimators based on weaker assumptions than the other? c)…arrow_forwardExample 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 9. 8. 8 7 6. 10 4 7 Marks in 2nd Test (Y) 8 7 10 8 10 9. 8 6. (a) Find the least square regression line of Y on X. / (b) Test the hypothesis that marks in the two tests are linearly related.arrow_forward0. In a statistical study, it is found that variables z and y are correlated as follows. Find the least squares regression line in this model.arrow_forward
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