In a simple linear regression, if we scale the data by a negative number, does the...

In a simple linear regression, if we scale the data by a negative number, does the t-statistic for the slope change to be the negative of the original result and the p-value for the slope change because the t-statistic for the slope changes?

Expert Solution

As it is given data so assuming that both X and Y are scale by negative so,

As we have seen is not effected so t statistics doesn't change and p value also doesn't change.

But alpha becomes negative but t statistics is depend on beta( slope parameter) so it doesn't change.

Please upvote if i'm able to help you it means a lot

Rahul Sunny answered 1 year ago

The simple linear regression of the data on $Sales and number of customers produced the following...

The simple linear regression of the data on $Sales and number of customers produced the following ANOVA output: ANOVA Source df SS MS F Significance F Regression 46833541 Residual Total 51360495 Complete as much of the ANOVA table as you need to answer the following two questions (Questions 18 and 19): The calculated value of the test statistic used to test the following null and alternative hypotheses Ho: The overall regression model is not significant Ha: The overall regression model...

When we estimate a linear multiple regression model (including a linear simple regression model), it appears...

When we estimate a linear multiple regression model (including a linear simple regression model), it appears that the calculation of the coefficient of determination, R2, for this model can be accomplished by using the squared sample correlation coefficient between the original values and the predicted values of the dependent variable of this model. Is this statement true? If yes, why? If not, why not? Please use either matrix algebra or algebra to support your reasoning.

What is a simple linear regression model? What does the value of the linear correlation coefficient...

What is a simple linear regression model? What does the value of the linear correlation coefficient tell us? Please type the answer as I have diffculties understanding handwritten answers. Thanks.

develop simple linear regression models for predicting sales as a function of the number of each...

develop simple linear regression models for predicting sales as a function of the number of each type of ad. Compare these results to a multiple linear regression model using both independent variables. State each model and explain R- square, significance F and P-values. Concert Sales Thousands of Thousands of Sales ($1000) Radio&TV ads Newspaper ads $1,119.00 0 40 $973.00 0 40 $875.00 25 25 $625.00 25 25 $910.00 30 30 $971.00 30 30 $931.00 35 35 $1,177.00 35 35 $882.00...

Consider the simple linear regression mode

Consider the simple linear regression modelYi = β0 + β1xi + εi, where the errors εi are identically and independently distributed as N (0, σ2).(a) If the predictors satisfy x ̄ = 0, show that the least squares estimates βˆ0 and βˆ1 are independently distributed.(b) Let r be the sample correlation coefficient between the predictor and response. Under what conditions will we have βˆ1 = r?(c) Suppose that βˆ1 = r, as in part b), but make no assumptions on...

Discuss the application of simple linear regression

Simple Linear Regression: Suppose a simple linear regression analysis provides the following results: b0 = 6.000, b1...

Simple Linear Regression: Suppose a simple linear regression analysis provides the following results: b0 = 6.000, b1 = 3.000, sb0 = 0.750, sb1 = 0.500, se = 1.364 and n = 24. Use this information to answer the following questions. (a) State the model equation. ŷ = β0 + β1x ŷ = β0 + β1x + β2sb1 ŷ = β0 + β1x1 + β2x2 ŷ = β0 + β1sb1 ŷ = β0 + β1sb1 x̂ = β0 + β1sb1 x̂ = β0 +...

Use Excel to estimate a simple linear regression model for the following data (Y is a...

Use Excel to estimate a simple linear regression model for the following data (Y is a dependent variable and X is an independent variable): Y X 0 -2 0 -1 1 0 1 1 3 2 Fill in Multiple Blanks: What is the slope of the estimated line? In your answer, show one (1) digit to the right of the decimal point, for example, 1.0, 1.2. Apply the appropriate rounding rule if necessary. What is the Y-intercept?

Complete a simple linear regression on the following data from a random survey of a random...

Complete a simple linear regression on the following data from a random survey of a random sample of free throws made out of 100: Age (in years) # of Free throws made (out of 100) 20 30 22 36 26 28 28 20 33 25 33 15 38 10 42 25 49 8 54 15 55 22 55 18 57 35 60 12 Provide the equation of the linear regression line (3 pts): Provide the coefficient of correlation (2...

Describe and explain what are the roles of simple linear regression in Data Science. Illustrate with...

Describe and explain what are the roles of simple linear regression in Data Science. Illustrate with a real-world application for each of the role described. Briefly explain how they perform the roles.( Detailed Explanation 1000 words)

Question