A production firm performed an evaluation on the customer perceptions on performance of the firm using...

 

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A production firm performed an evaluation on the customer perceptions on performance of the firm using a Linkert scale with variables X₂ = Competitive pricing and X3 = Price flexibility. Each customer's perceptions on the perfomance of the firm were measured on a graphic rating scale, where a 10-centimeter line was drawn between the endpoints, labelled "Poor" and "Excellent,". As part of the survey, customers indicated their perceptions by making a mark anywhere on the line. The location of the mark was electronically observed and the distance from 0 (in centimetres) was recorded. The result was a scale ranging from 0 to 10, rounded to a single decimal place. Below is the logistic regression analysis output for predicting the customer location (X₁ = Area [0:1]) in response to perceptions on performance of the firm. The area is 0 for Johannesburg and 1 for Pretoria. Table I -Log Likelihood Table II Test Likelihood Ratio Score Wald Table III Statistical Measures of overall Model Fit improvement Step 1: X₂ entered Step 2 (Final Model): X3 entered Model Fit improvement: Reduction in -2 Log Likelihood (Base Model -2LL 82.108) Reduction in Reduction in - Pseudo R² Measure Cox and Snell R² Nagelkerke R² Pseudo R2 i. ii. iii. iv. -2LL 25.136 V. chi- Square 25.1363 21.3297 15.471 Testing the Global null Hypothesis chi- Square Significance .342 .459 .306 Independent Variable B X₂ Competitive Pricing X3 Price Flexibility Constant .000 Pr> DF chiSq 2LL 17.011 1 < .0001 1 <.0001 1 <.0001 Pseudo R² Measures of Model Fit Step 1: X₂ entered 42.1477 31.3228 14.1772 DF 222 2 Significance .000 Table IV Regression analysis output for predicting customer's location in response to customers perceptions on evaluation of the firm. Std. Pr> chisq error Wald 1.079 9.115 .357 1.844 .639 214.192 3.712 8.331 14.614 B = logistic coefficient, Exp (B) = exponentiated coefficient. <.0001 <.0001 0.0008 Step 2 (Final Model): X3 entered .505 .677 .513 DF Sig. exp (B) 1 .003 2.942 6.321 1 .004 1 .000 .000 STA4820/017/0/2022 Write the fitted logistic regression model using table IV. What is the probability of a customer being from Pretoria, when X₂ is 7 and X3is 6? What does the intercept from the model tell you? Formulate the global null hypothesis and give conclusion based on table II results. Interpret model fit based on tables I and III. 3 € (4) (4) (4) A production firm performed an evaluation on the customer perceptions on performance of the firm using a Linkert scale with variables X₂ = Competitive pricing and X3 = Price flexibility. Each customer's perceptions on the perfomance of the firm were measured on a graphic rating scale, where a 10-centimeter line was drawn between the endpoints, labelled "Poor" and "Excellent,". As part of the survey, customers indicated their perceptions by making a mark anywhere on the line. The location of the mark was electronically observed and the distance from 0 (in centimetres) was recorded. The result was a scale ranging from 0 to 10, rounded to a single decimal place. Below is the logistic regression analysis output for predicting the customer location (X₁ = Area [0:1]) in response to perceptions on performance of the firm. The area is 0 for Johannesburg and 1 for Pretoria. Table I -Log Likelihood Table II Test Likelihood Ratio Score Wald Table III Statistical Measures of overall Model Fit improvement Step 1: X₂ entered Step 2 (Final Model): X3 entered Model Fit improvement: Reduction in -2 Log Likelihood (Base Model -2LL 82.108) Reduction in Reduction in - Pseudo R² Measure Cox and Snell R² Nagelkerke R² Pseudo R2 i. ii. iii. iv. -2LL 25.136 V. chi- Square 25.1363 21.3297 15.471 Testing the Global null Hypothesis chi- Square Significance .342 .459 .306 Independent Variable B X₂ Competitive Pricing X3 Price Flexibility Constant .000 Pr> DF chiSq 2LL 17.011 1 < .0001 1 <.0001 1 <.0001 Pseudo R² Measures of Model Fit Step 1: X₂ entered 42.1477 31.3228 14.1772 DF 222 2 Significance .000 Table IV Regression analysis output for predicting customer's location in response to customers perceptions on evaluation of the firm. Std. Pr> chisq error Wald 1.079 9.115 .357 1.844 .639 214.192 3.712 8.331 14.614 B = logistic coefficient, Exp (B) = exponentiated coefficient. <.0001 <.0001 0.0008 Step 2 (Final Model): X3 entered .505 .677 .513 DF Sig. exp (B) 1 .003 2.942 6.321 1 .004 1 .000 .000 STA4820/017/0/2022 Write the fitted logistic regression model using table IV. What is the probability of a customer being from Pretoria, when X₂ is 7 and X3is 6? What does the intercept from the model tell you? Formulate the global null hypothesis and give conclusion based on table II results. Interpret model fit based on tables I and III. 3 € (4) (4) (4)

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Answer i Logistic regression is an extension of simple linear regression Where the dependent variabl... View the full answer