Chapter 9, Section 1, Exercise 006 Computer output for fitting a simple linear model is given...

Chapter 9, Section 1, Exercise 006

Computer output for fitting a simple linear model is given below. State the value of the sample slope for this model and give the null and alternative hypotheses for testing if the slope in the population is different from zero. Identify the p-value and use it (and a 5% significance level) to make a clear conclusion about the effectiveness of the model.

The regression equation is Y⁢=83.2-0.0133X.

Predictor	Coef	SE Coef	T	P
Constant	83.23	11.94	6.97	0.000
X	-0.01327	0.01106	-1.20	0.245

Sample slope:

p-value:

Expert Solution

As per the given information,

The regression equation is Y=83.23 - 0.0133X.

Predictor	Coef	SE Coef	T	P
Constant	83.23	11.94	6.97	0.000
X	-0.01327	0.01106	-1.20	0.245

The significance level is 0.05.

Sample slope: - From the above output, the slope coefficient is – 0.01327 which is approximately equals to - 0.0133.

The researcher wants to test if the slope in the population is different from zerot.

The null and the alternative hypothesis is,

p-value: From the above output, the p-value is 0.245.

Since the p-value (0.245) is greater than the significance level 0.05, so the researcher rejects the null hypothesis.

Therefore, it can be concluded that there is not sufficient evidence to support that the slope in the population is different from zero. Thus, the result of the study is statistically insignificant; that is, the model is not statistically effective.

orchestra answered 1 year ago

Chapter 9, Section 1, Exercise 005 Computer output for fitting a simple linear model is given...

Chapter 9, Section 1, Exercise 005 Computer output for fitting a simple linear model is given below. State the value of the sample slope for the given model. In testing if the slope in the population is different from zero, identify the p-value and use it (and a 5 % significance level) to make a clear conclusion about the effectiveness of the model. The regression equation is Y ⁢=87.0 -6.9 X . Predictor Coef SE Coef T P Constant 87.013...

Chapter 9, Section 3, Exercise 057 Two intervals are given, A and B, for the same...

Chapter 9, Section 3, Exercise 057 Two intervals are given, A and B, for the same value of the explanatory variable. A: 3.9 to 6.1; B: 2.6 to 7.4 (a) Which interval is the confidence interval for the mean response? A or B? Which interval is the prediction interval for the response? A or B? (b) What is the predicted value of the response variable for this value of the explanatory variable? Enter the exact answer. The predicted value is

In a normal simple linear regression model you are given that the variance of the error...

In a normal simple linear regression model you are given that the variance of the error term is 4. Four observations are taken, in which the X values are X=-2,1,2,3. Calculate the variance in the estimate for the slope coefficient.

Remind yourself about linear least squares fitting in section 3.2 of the lab manual, and then...

Remind yourself about linear least squares fitting in section 3.2 of the lab manual, and then work through the following. In a particle physics experiment, there are six detectors at positions x = 10; 14; 18; 22; 26; and 30cm. These detectors measure the y positions of the trajectory of a charged particle to be 2.02; 2.26; 3.24; 3.33; 3.92; and 4.03 cm, respectively (i.e., the first position is (10,2.02), the second position is (14,2.26), and so on). The errors...

Curve-fitting Project - Linear Model Instructions For this assignment, collect data exhibiting a relatively linear trend,...

Curve-fitting Project - Linear Model Instructions For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described...

This exercise will investigate some inferential questions about the intercept β0 from a simple linear model....

This exercise will investigate some inferential questions about the intercept β0 from a simple linear model. a. Show that E(Ȳ) = β0 + β1x̄. b. Show that 0 is an unbiased estimator for β0. c. Calculate the variance of 0. Hint: Recall that Ȳ and 1 are independent.

1. Following is the R output when fitting regression model of X= miles run per week...

1. Following is the R output when fitting regression model of X= miles run per week and Y= weight loss after a year. Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 64.28 8.11 7.93 0.015 * X 1.23 0.63 1.96 0.188 ----------------- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 6.773 on 2 degrees of freedom Multiple R-squared: 0.6586, Adjusted R-squared: 0.4879 F-statistic: 3.858 on 1 and 2 DF, p-value: 0.1885...

Chapter 1, Section 3, Exercise 092 Do Antidepressants Work?

1, Work problem on Page 9-47, Question 5. Given the computer output shown following for testing...

1, Work problem on Page 9-47, Question 5. Given the computer output shown following for testing the hypotheses Ho: (μ1 - μ2) = 0 Ha: (μ1 - μ2) > 0 What conclusion would you draw, with α = .10? What assumption(s) did you make in answering this question? Variable: X SAMPLE N Mean Std Dev Std Error 1 32 77.1 6.03 1.07 2 58 75.2 4.21 0.55 Variances T DF Prob > ∣T∣ Unequal 1.58 48.0...

Fitting a linear model using R a. Read the Toluca.txt dataset into R (this dataset can...

Fitting a linear model using R a. Read the Toluca.txt dataset into R (this dataset can be found on Canvas). Now fit a simple linear regression model with X = lotSize and Y = workHrs. Summarize the output from the model: the least square estimators, their standard errors, and corresponding p-values. b. Draw the scatterplot of Y versus X and add the least squares line to the scatterplot. c. Obtain the fitted values ˆyi and residuals ei . Print the...

Question