Question 1

The pens were exposed to five different advertisement strategies. The first treatment focused on greatly underselling the pen characteristics (A) the second focused on slightly underselling the pen’s characteristics, the third treatment focused on slight overselling of the pen’s characteristics (C), the fourth advertisement strategy greatly oversells the characteristics of the pen (D) while the last advertisement strategy attempted to correctly state the characteristics of the pen (E).  Different ratings on the durability, appearance and writing performance of the pens were provided by the 30 respondents involved in the study.

Analysis of the responses provided, using One Way ANOVA analysis shows that there is significant difference in the rating given for each of the five advertisement categories. At 0.05 level of significance, a p-value of 0.00001 is attained, meaning there is a significant difference in the ratings provided.

Further post hoc analysis using the t-test shows that there is significant difference between the various advertisement strategies implemented by the organization. There is a significant difference between advertisement A and C (p=0.001), advertisement A and D (p=0.0000), advertisement B and C (p=0.002), advertisement B and D (p=0.000), and advertisement D and E (p=0.004).

Question 2

Multicollinearity in regression analysis refers to a situation where one independent variable can be predicted from the others with a significant level of accuracy. Under this situation the coefficient estimate of the regression may unevenly change with a small change in the data or the model.

The presence of highly correlated data in a given sample shows that there is a high possibility of multicollinearity. The effects of multicollinearity can be controlled by removing highly correlated independent variables from the mode or using partial least square regression that aim at cutting the numbers of the independent variables into smaller components thus limiting the correlation nature of the predictor variables.

The study variables are

Dependent variable-home price

Independent variables-Size, whether there is a pool, attached to a garage, distance from the center and number of bathrooms

Y=bX+A+B+C

Correlational analysis of the independent variables shows that size and baths are highly correlated (p=0.02), also, the number of bedrooms and whether a pool is available variables are also highly correlated (p=0.00). The correlation between the independent variables shows a possibility of multicollinearity in any case all the predictor variables are included in the regression process.

The best regression model will be one where the highly correlated variable is eliminated from the regressions. In this case the regression analysis will be conducted with the exclusion of the pool and baths variables

The results obtained is significant indicating that the price of the houses is largely determined by the size of the houses, the distance, the availability of a garage and the number of bedrooms in the house. The stepwise regression analysis shows that the size of the house is the major determinant of the price of the houses. While other predictor variables such as presence of a garage, a pool, the distance and the number of bedrooms also has effects on the cost of the houses, their implications are thus not significant as that of the size of the house.

Question 3

Logistic regression refers to the analysis conducted with a binary dependent variable. Similar to other forms of regression analysis, the logistic regression is referred to as a predictive analysis. The approach is adopted when describing data and determining the relationship between one binary variable and another nominal or ordinal variable. Also, the regression analysis can be conducted when determining the relationship between the dichotomous dependent variable and other ratio-level independent variable.

1. In (odds of participation) = 5.78+1.94(car)-0.068(distance)-0.06(age)
2. The probability that the a 65-year old patient will take part in the rehabilitation if he travels 20 km to the rehabilitation and has a car is 92%
3. The probability that a 65-year old patient will participate in the rehabilitation if he travels for 20 kilometers and has no car is 63%
4. Based on the findings attained, it can be deduced that having a car enhances the possibility of a patient to take part in the rehabilitation

• At a significance of 0.05 it is observed that the distance covered by the patient and the age of the patient all have significant effects on possibility of participating in the rehabilitation
• Owning a car is the greatest determinant of whether a patient participates in the rehabilitation or not

(Odds increase by 7 times)

Question 4

1. Ln (Odds of Purchase) = 1.23 + 2.22(subscription) – 0.03(Age)

• The coefficient for age is -0.03 and it means that if the age of the customer increases by 1 year, he/she has a 1.03 times possibility of not making a purchase, if the said customers had subscribed for the newsletter then he/she will have 9 times more chance of making a purchase

c. The probability that a 35-year old customer will purchase the new organic products is 91%