Question

Question 312 marks An study was conducted using data from pedometers of 68 randomly selected participants. The researchers wanted to know if the number of steps taken by a participant (Steps) could be predicted using the time they spent walking (Minutes). The data are available on MyUni in the file Steps.csv. 2 (a) Produce a scatterplot of Steps vs Minutes and describe any relationship between these two variables. (b) Perform a linear regression analysis on this data in MATLAB and then answer the 2 4 following questions. Include your output from MATLAB in your assignment i. Write down the equation of the line of best fit ii. Perform an appropriate hypothesis test to determine whether there is a statisti- cally significant linear relationship between Steps and Minutes at the 5% level. Include the appropriate null and alternative hypotheses, test statistic, and conclusion. Define any parameters you use. P-value, e) Determine, with accompanying plots, if the assumptions of the linear regression model are reasonable for this set of data.

Answer 1

a) The scatter plot graph is drawn for Steps Vs Minutes which is shown below scatter plot 50 40 30 20 10 6000 steps 10000 12000 the above plot shows the linear relationship between steps and minutes. b) Linear regression is done its result ts standard Error tstat P-value Lower 95% r95% Lower 95.0% U 95.0% Intercept9 9.705006283. 3.50990773 2.76503 0.00737216.71276317 -2.697249392 -16.71276317 -2.697249392 0.005596929 0.000610876 9.162142 2.24E-13 0.004377276 0.006816581 0.004377276 0.006816581 minutes the best fitted line is given as Y(steps) - ab XIminutes) Y=-9.705 + 0.0055 X. The hypothesis are HO: There is no linear relationship between Steps and Minutes walked. H1: There is linear relationship between Steps and Minutes walked the significance level is fixed at 5%

the above results shows p value as 0.007 which is less than 0.05 so there is no significant evidence to accept null hypothesis, therefore there is linear relationship between steps and minutes walked. d) the plot of linear regression is as follows 60 p scatter plot 0.0056x-9.705 50 40 n 30 E 20 10 2000 4000 6000 8000 .10 steps