In exercise 7, the data on y = annual sales ($1000s) for new customer accounts and x = number of years of experience for a sample of 10 salespersons provided the estimated regression equation yˆ = 80 + 4x. For these data x = 7, o(xi − x)2 = 142, and s = 4.6098. a. Develop a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience. b. The company is considering hiring Tom Smart, a salesperson with nine years of experience. Develop a 95% prediction interval of annual sales for Tom Smart. c. Discuss the differences in your answers to parts (a) and (b).

Forest bathing, also called Shinrin-yoke, is the practice of taking short, leisurely walks in a forest to enhance positive health. To test if forest bathing and mood are related, a clinical psychologist records the time spent forest bathing in minutes (X) and the corresponding change I mood using a standard self report affect grid (Y) among 8 patients with a history of depression. The data are given in the following table. times spent forest bathing (in minutes) change in mood X Y 32 +24 24 +20 28 +25 17 +22 12 +16 Compute the method of least squares to find the equation of the regression line. Use the regression equation computed in part (a) to determine the predicted change in mood of a person who spends 20 minutes forest bathing.

While performing searches on the Internet to find accommodation, Jasmine realized that the cost of a housing unit seems to be related to the number of inhabitants of the municipality where the unit is located. She noted the following data. She represented the data in a scatter plot, where she drew a line of best fit passing through the mean point of the distribution. If Jasmine considers that a linear correlation exists between these two variables, what should be the mean monthly rent of a 4½-room unit in a municipality with a population of approximately 250 000? Justify your answer algebraically.

Suppose the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Sup-pose we have another investment Y with a 1.5% mean monthly return and standard deviationof 6%. Which of the two investments o ers less risk in terms of investment.

A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow:   Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800    Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary.         Find the equation of the least-squares regression line. (Round to two decimal places)

An exercise scientist wants to know if there is a relationship between explosive leg power and standing jump height.  To determine if a relationship exists, a group of 30 participants' (N = 30) Leg power was measured  by recording each participants' single squat weight max (in pounds). Next, each participant was asked to perform a standing jump and their Jump height was recorded (in meters). Using the variables “Leg power” and “Jump height”, conduct a Pearson's Correlation, at α = 0.05, to determine if leg power and jump height are correlated. What does this type of correlation indicate about how leg strength and jump height change together?    A. Both leg strength and jump height increase and decrease together B. There is no relationship between leg strength and jump height C. As leg strength increases, jump height decreases D. As jump height increases, leg strength decreases

A study is conducted to investigate the association between income level and political party affiliation in the USA. Income level has 5 levels: Lowest (lowest 20-th percentile), low, middle, high, and very high (top 20-th percentile). Political party has 3 categories: Democratic (D), Independent (I), and Republican (R). A baseline category logit multinomial is fit on the 3 response categories using covariate of income level as ordinal (with scores 1, 2, 3, 4, and 5 for the categories lowest, low, middle, high and very high respectively). Base category of response is Independent. The fitted model is log(ˆπD/πˆI ) = 3.3 − 0.2x and log(ˆπR/πˆI ) = 1.0 + 0.3x, where x=1,2,3,4,5 (poverty levels as numeric/ordinal), πD is the probability of being Democrat, πI is the probability of being Independent, and πR is the probability of being Republican. a. Comparing the chances/probability of being Republican to Independent, interpret the effect of income level increases on the odds (of being…

The following regression is fitted using variables identified that could be related to student requestedloan amount, LOAN-AMT($) for returning students of a certain University. ????−??? = ? + ? ?????? + ? ???? + ? ????Where ACCEPT = the percentage of applicants that was accepted by the university, PREV = previous loan amount and OUTS =outstanding loan amountThe data was processed using MNITAB and the following is an extract of the output obtained:EXHIBIT 2Predictor Coef StDev T PConstant -26780 6115 * 0.000ACCEPT 116.00 37.17 3.14 0.003PREV -4.21 14.12 -0.30 **OUTS 70.85 15.77 4.49 0.000S = 2685 R-Sq = 69.6% R-Sq(adj) = 67.7%Analysis of VarianceSource DF SS MS F PRegression 3 808139371 269379790 37.37 0.00Residual Error 49 353193051 7208021Total 52 1161332421a)What is dependent and independent variables? b)Fully write out the regression equation c)What is the sample size used in this investigation? d)Fill in the blanks identified by ‘*’ and ‘**’. e)Is β significant, at the 5% level of…