After running a regression on 60 monthly observations of a fund's returns on thereturns of a stock market index, you find the estimate of the slope coefficient of 1.18with a standard error of 0.39. You are interested in testing the hypothesis of whetherthe slope is equal to 1. What is the t-statistic for this hypothesis test?(Bonus thinking question: can you reject the null hypothesis that the slope 1 at a 5%confidence level?)

Given: Sample size, n=60 Estimate of slope coefficient, β^1=1.18 Standard error is, seβ^1=0.39

Answered: After running a regression on 60…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 17HP

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For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
In simple linear regression, most often we perform a two-tail test of the population slope 1 to determine whether there is sufficient evidence to infer that a linear relationship exists. The null hypothesis is stated as:
Togetherness Are good grades in high school associ-ated with family togetherness? A simple random sample of 142 high-school students was asked how many mealsper week their families ate together. Their responses produced a mean of 3.78 meals per week, with a stand-ard deviation of 2.2. Researchers then matched these responses against the students’ grade point averages. Thescatterplot appeared to be reasonably linear, so they went ahead with the regression analysis, seen below. No appar-ent pattern emerged in the residuals plot. Dependent variable: GPAR-squared = 11.0%s = 0.6682 with 142 - 2 = 140 dfVariable Coefficient SE(Coeff)Intercept 2.7288 0.1148Meals/wk 0.1093 0.0263 a) Is there evidence of an association? Test an appropri-ate hypothesis and state your conclusion. b) Do you think this association would be useful inpredicting a student’s grade point average? Explain.c) Are your answers to parts a and b contradictory?Explain.
Write the formula for the estimated regression line and interpret the slope of the estimated regression line, the intercept of the estimated regression line- Is it meaningful?, and the estimated R2. Based on the fitted regression model, what is the predicted ATST for a child who is 7 years old? What is the correlation between AGE and ATST? Does the residual plot suggest that the fitted regression line is inappropriate for these data? Explain why or why not. Suppose that a new subject is added to the study data and that subject is 12.5 years old with an ATST of 580 minutes. If the regression model were to be refit with this additional data point, would the new slope be greater than or less than -14.041? Justify your response.
The accompanying table lists systolic blood pressures (mm Hg) and diastolic blood pressures (mm Hg) of adult females. Find the (a) explained variation, (b) unexplained variation, and (c) prediction interval for a systolic blood pressure of 118 mm Hg using a 99% confidence level. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Systolic Diastolic 127 69 103 65 130 73 104 64 157 74 97 51 155 90 111 69 124 68 112 75 103 60 128 67
a. Can you construct a 95% confidence interval for the y intercept for the regression equation then justify the correlation between time and duration? b. Also, what are the chances of seeing a relationship between time and duration as strong or stronger than this, when in fact there was none?

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