Answer to Question #165048 in Statistics and Probability for Sunny

Question

Brand Kidzania wanted to study the impact of its brand personality on the customer brand engagement. The five elements of brand personality are Sincerity, Excitement, Competence, Sophistication, Ruggedness. The multiple regression analysis of the data collected is as follows:

personality are Sincerity

Model Summary

Model R R square Adjusted R square std. error of the estimate

1 .928^a .863 .835 3.42991

Anova

Model Sum of squares df mean square F Sig

1 Regression 134.904 5 26.981 2.293 .038^b

Residual 2023.455 172 11.764

Total 2158.360 177

coefficient

Unstandardized standardized

coefficients coefficient

Model B std. error Beta t Sig

1 ( constant) 13.318 1.059 12.577 .000

Sincerity -.226 .118 -2.54 -1.921 .046

Excitement .319 .141 .348 2.267 .025

competence -0.52 .121 -0.59 -415 .679

sophistication .059 .165 .050 357 .722

ruggedness .127 .187 .074 . 687 .499

a. is this model significant ? State the null and alternate hypothesis.

b. which are the independent (IV) and dependent variable (DV)?

c. Which independent variables can be concluded as the predictors of dependent variables and why?

d. what is the percentage of variation explained by independent variable in dependent variable?

e. Write the regression equation

f. interpret the partial regression coefficients.

g. what is the sample size?

Answer 1

Answer:

a)

Hypothesis,

Ho: The five elements of brand personality are Sincerity, Excitement, Competence, Sophistication, Ruggedness are Statistically significant.

H1: The five elements of brand personality are Sincerity, Excitement, Competence, Sophistication, Ruggedness are not Statistically significant.

Here Calculated value of F is 0.038

And tabulated value of F at 5 and 172=> infinite d.f is

 3.02

Cal F< Tab F so we fail to null hypothesis hence it is Statistically significant. 

b)

Brand personality is dependent variable (Y)

 The five elements of brand personality are Sincerity, Excitement, Competence, Sophistication, Ruggedness are independent variables .

 

(c). Sincerity and excitement can be concluded as the predictors of dependent variable because these p values are less than 0.05

d)

The percentage of variation is explained by independent variable in dependent variable is given by the value of R².

From the output, the value of R² is 0.863

This, the percentage of variation is explained by independent variable in dependent variable is 86.3%.

 

e)

Regression Equation:

From the output,

• Constant:13.318
• Sincerity:-0.226
• Excitement: 0.319
• Competence: -0.52
• Sophistication: 0.059
• Ruggedness:0.127

Therefore, the regression equation is,

Brand personality=13.318-0.226Sincerity+0.319Excitement-0.52Competence+0.059Sophistication+0.127Ruggedness.

f)

Interpretation of regression coefficients:

• The value 13.318 represents the constant change in Brand personality.
• The value -0.226 represents there is a 0.226 units decrease in Brand personality as 1 unit increase in Sincerity.
• The value 0.319 represents there is a 0.319 units increase in Brand personality as 1 unit increase in Excitement.
• The value -0.52 represents there is a 0.52 units decrease in Brand personality as 1 unit increase in Competence.
• The value 0.059 represents there is a 0.059 units increase in Brand personality as 1 unit increase in Sophistication.
• The value 0.127 represents there is a 0.127 units increase in Brand personality as 1 unit increase in Ruggedness.

g)

Here,

Total degree of freedom= n-1

                     =215

Therefore, sample size, n=216