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- Tom has been gathering data concerning the cost of a spa treatment, y', during the before Valentine's Day. The only independent variable that he has considered is the number of minutes, "x," in the treatment. Suppose Tom collects data on the relationship between the number of minutes in a treatment and the resulting cost of we the treatment. Tom finds that the correlation between cost and number of minutes is strong and positive. Therefore, he has performed a linear regression analysis on his data. His results are that the constant "a" is 35, and the coefficient "b1" for the independent variable is 1.3. Which of the following is the correct linear regression equation that would allow Tom to predict the cost of a spa treatment given the number of minutes? Oy = 78x + 35 Oy' = 1.3x + 35 %3D Oy = 78x - 1.3 %3D OY = -1.3x - 35A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds), Two variables thought to affect weight loss are client's length of time on the weight-loss program and time of session These variables are described below: Y-BO+B1'X+82'D 83'X'D+E Y-Weight loss (in pounds) X- Length of time in weight-loss program (in months) D-1 if morning session. O if not in terms of the Bs in the model, what is the difference between the weight loss of an individual who has spent 3 months in the program when attending the morning session, and an individual who has spent 2 months in the program when attending the evening session? OB1+83 OB1+82-83 OB1+82+283 O81+82+383Construct the equation of the regression line. An editing firm compiled the following table which lists the number of pages contained in a piece of technical writing and the cost of proofreading and correcting them (in dollars). Assume there is a significant linear relationship between X and Y and construct the equation of the linear regression line. Number of Pages, x 7 12 4 14 25 30 Cost, y 128 213 75 250 446 540 a.) y^= 17.9(x) + 1.6 b.) y^= 7.1(x) + 15.4 c.) y^= 15.4(x) + 7.1 d.) y^= 1.6(x) +
- 8- According to the summary result of linear regression model between A and B obtained from R given below, we can fit a regression line. Assume that A has any value. If we decrease the value of A by 3, how would Y be affected? Call: Im (formula = B - A) Residuals: Min 10 Median 30 Маx -16.340 -10.793 -9.653 -8.502 58.325 Coefficients: Estimate Std. Error t value Pr (>[t]) (Intercept) 19.6315 20.6457 0.951 0.373 A 9.9609 0.3717 26.800 2.58e-08 *** --- Signif. codes: O *** 0.001 1** 0.01 1** 0.05 '.' 0.1 '' 1 Residual standard error: 26.46 on 7 degrees of freedom Multiple R-squared: 0.9903, Adjusted R-squared: 0.989 F-statistic: 718.2 on 1 and 7 DF, p-value: 2.58le-08 a) 49.5142 decrease b) 29.8827 increase c) 58.8945 decrease 29.8827 decrease 58.8945 increaseWe are interested in estimating the following model log(wage) = Bo + Bieduc + Bzexper + u where • wage=hourly wage, in US dollars; • educ=number of years of education; • exper=number of years of work experience. The variable ctuit is the change in college tuition facing students from age 17 to age 18 and is used as an IV for educ. We run the first stage regression for educ and get the following output: Source s df MS Number of obs 1,230 F (2, 1227) 550.19 Model 3220.84426 2 1610.42213 Prob > F 0.0000 Residual 3591.43541 1,227 2.92700523 0.4728 R-squared Adj R-squared 0.4719 Total 6812.27967 1,229 5.54294522 Root MSE 1.7108 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] ctuit -.1859575 .0608175 -3.06 0.002 -.3052752 -.0666398 exper -.521161 .0157156 -33.16 0.000 -.5519933 -.4903286 _cons 18.63905 .1757961 106.03 0.000 18.29415 18.98394 Is the assumption of instrument relevance satisfied? Why yes, or why not?For the linear regression model Y = bo + b1(X): The p-value for the intercept is large: about 0.98 The p-value for the slope is very small: less than 2 times 10^(-16) What can we conclude? Since the p-value for the intercept is large, we can conclude that there is not a strong correlation between X and Y. Since the p-value for the intercept is large, we can conclude that there is a very strong correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very weak correlation between X and Y. Since the p-value for the slope is very small, we can conclude that there is a very strong correlation between X and Y. We are not able to assess the strength of the correlation between X and Y with the output provided.
- The estimated regression equation for a model involving two independent variables and 10 observations follows. y = 33.0798 + 0.6071x1 + 0.7058x2 a. Interpret b₁ and b2 in this estimated regression equation (to 4 decimals). b₁ = - Select your answer - b₂ = - Select your answer - b. Estimate y when *₁ = 180 and ₂ = 310 (to 3 decimals).Suppose you obtain the following regression model, E[y]=20+53*x +33*x^2. What is the impact of a 63 unit change of x on the expected value of y when x is at its mean of 54?A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 12 26 5 28 11 24 20 21 16 Money 37 84 34 84 53 92 72 92 75 The equation of the linear regression line is: ˆyy^ = + xx (Please show your answers to two decimal places) Use the model to predict the amount of money spent by a customer who spends 20 minutes at the store.Dollars spent = (Please round your answer to the nearest whole number.)
