Question

An online gaming company collects data on the amount of time 250 users spend playing a game and the amount they spend in dollars on in-game purchases. A statistician working for the company runs a regression analysis relating the total purchase amount to the minutes spent playing (Play). The output of this analysis is shown below:

Predictor            Coeff                   SE-coeff              T                          P

Constant            .8911                  .26411                 3.3740               0.001

Excercise            .1720                  .07861                 2.1880               .030

S= 0.461              R-Sq= 72.6%       R-Sq(adj)= 72.5%

(A) What is the predicted amount spent by a user who plays for 30 minutes?

(B) Calculate the residual for a user who plays for 45 minutes and spends a total of $7.50.

(C) Calculate a 95% confidence interval for the slope of the regression line, given that the critical value for t is 1.97.

(D) Using the information provided, determine whether there is sufficient evidence to say that there is a significant relationship between the minutes spent playing and the amount spent, at the 5% level.

Answer 1

a) The predicted amount spent by a user who plays for 30 minutes is computed here using the coefficients here as:

Therefore $6.0511 is the required predicted amount spent here.

b) The predicted amount spent for 45 minutes is computed here as:

Therefore the residual here now is computed as:
= Observed Value - Predicted Value

= 7.5 - 8.6311

= -$1.1311

Therefore = -$1.1311 is the required residual here.

c)The standard error of the coefficient of slope here is given to be 0.07861. The slope coefficient here is 0.1720. Therefore the confidence interval for the given t test statistic here is obtained as:

This is the required confidence interval here.

d) As the above computed confidence interval dont contain 0, this means that at 5% level of significance, we can reject the null hypothesis here and conclude that we have sufficient evidence that there is a significant relationship between the minutes spent playing and the amount spent,